That the participants in the pygmy wars used the same weapons as WWI doesn't mean they were similar in how they were fought. Reading the memoirs of men who participated in both, they always stress how very different they were. There is an anecdote where a Kornilov officer was astonished when he turned up to a unit attempting to abide by WWI regulations, knowing that the Reds would not fight in a WWI style that the White unit would be almost instantly defeated (which it was).
By "WWI" below I mean the fronts of Europe, not the side theatres like Palestine. I would also argue that those should use period specific rules too.
The biggest difference is purely troop densities: a normal RCW Division, say 5,000 men, might hold 10 km of front, and often more. Obviously that didn't mean they were strung out across that width, so battles became about holding positions of strength – villages, river crossings, rail junctions, rather than front lines as such. Turning actions were standard. The result was that the RCW was a war of movement and improvisation. Troops usually operated independently, often with only the most sketchy operational planning.
Troops dug trenches, but rarely trench lines, and didn't generally have enough wire or entanglements to protect them properly. Other than attacks on key cities or rail hubs, any strong positions were simply by-passed. Even in defensively lines defending major cities, the troops defending them were frequently unable to hold even briefly if the attackers had any sort of heavy artillery or armour support.
Even the Whites in the RCW were haphazardly commanded, and it got worse with the other armies. WWI units largely obeyed orders, for a start. In WWI you should assume an attack by units across the front would be co-ordinated, whereas for the RCW you should assume the exact opposite. A WWI army might have synchronised watches to ensure an attack was done to plan. The Russians just waited till they heard some shooting and then played it by ear.
Commanders, even very senior ones, would disobey direct instructions. The Reds started by far the worst in this regard, but worked hard on correcting this. But Budenny was a law unto himself to the end. Similarly, White commanders might disobey orders, for good or bad reasons.
RCW armies did not retire fighting for any length of time. They held their ground, pulled back to new positions (usually quite a long way back) or fled. Armies would often fall back several hundred kilometres in a week without significant fighting.
WWI units kept in close contact with those beside them, coordinating their actions. RCW units usually operated independently in columns, often with only the bare outlines of a plan. (This advantaged the Whites somewhat, because they tended to have decent cavalry with their infantry units, while the opposing Red infantry columns generally did not.) Each column had to be trusted to come to the aid of their neighbours without being ordered, which meant the commanders tended to be picked on their initiative and boldness. This led to most field commanders being very young, and not bothered by regulations or formal procedures.
As the war went on, the Civil War commanders saw that winning was as much psychological as about physical. They started doing things that they knew were wrong under standard conditions – they would launch offensives with scant regard to protecting their flanks, because they knew if they broke the enemy line and forced a general retreat that their flanks would remain unbothered. They might fire HE rather than shrapnel in open field, because the psychological effects of the explosions were more valuable than the deadly but less visible shrapnel.
Good RCW generals tried to win without fighting, by turning flanks or by surprise attacks. Bloody frontal assaults by lines of units were rare. Night attacks, or at least raids, were common.
The civil war generals also discovered that defending usually did not work – they sought to move to the attack at any opportunity. If forced to defend, they would keep only the thinnest possible front line, and then counter-attack any breakthrough with reserves. The Poles in early 1920 still mostly defended with a WWI paradigm of defending a front line: the result was that the Soviets broke through them easily every time, forcing massive retreats.
WWI rules assume effective indirect artillery fire, with large amounts of ammunition by trained officers. Some of the RCW artillery units knew how to do that, but in practice they rarely did. The RCW had almost entirely firing in open field, with limited ammunition and officers who often were not well trained. If your rules make it an advantage to be firing from the rear, as it was in WWI, then they will give a completely wrong feel to the RCW.
The Poles did try for a while to use artillery as if it were still WWI. They would set up communications nets, have pre-allocated beaten zones by battery, etc. What tended to happen was by the time they set it all up, the Reds would break through their lines and it would all be wasted effort. Eventually they discovered that they too had to have their guns up in the front lines, giving direct support.
The Reds and Whites eventually settled on using their artillery in penny-packets. Battalions might have two guns in support. They even sent artillery with their scouting parties.
The effect of the guns was quite different too. WWI units would take a bombardment for hours on end, days even, from huge batteries, and remain in place. RCW units would flee after a short bombardment from a couple of batteries.
However, while artillery was very powerful in the RCW, the effect was reduced by the perpetual lack of ammunition, so that artillery could rarely expend ammunition with long pre-battle bombardments. Very often they could barely fire in hot battle because they started to run out of ammunition. (I limit the amount they can fire in my games, even on the tabletop, to limit long-range fire – they almost always waited to effective range before even starting to fire.)
WWI rules will have conscript infantry. That's your starting point for RCW, and mostly it should go down from there. Unless you read about it, you don't really get an idea just how awful much of the RCW infantry was, both in morale and combat ability. Early in the war White officer units sometimes forced Reds out of covered positions in villages just by walking up to them – while not taking cover and without shooting. I can't imagine any WWI rules would ever allow for a unit to walk on up to a defended village and win.
The amount of rifle power out of an RCW unit, even a good one, should be less than half of a WWI one. That leads to units fighting at much shorter ranges. It was a matter of willpower who won, not shooting. So Red sailor units were effective, despite having no training in land warfare (particularly the commanders). The Czechs were hugely effective in 1918 Siberia simply because they were organised and had an esprit de corps, even while fighting for a cause in which they had little interest.
Most RCW infantry units in trouble will rout or surrender, not retreat fighting, and would not reform until after the battle. Indeed, most units would retire at the first sign that the enemy had appeared in their rear or that armour has appeared in front of them. That the White "officer" units did not do this, was part of what made them so effective.
MGs were the prime means of delivering firepower and could keep most infantry pinned almost indefinitely. RCW rules should increase their effectiveness relative to rifle fire.
Like the artillery, running out of ammunition was a constant problem. The result was the ammunition was usually conserved, and WWI practices that were heavy on ammunition stopped being used (such as harrassing fire and permanent suppression using constant MG fire).
Good RCW cavalry should be able to frontally charge an isolated infantry unit and defeat it, at least some of the time.
Cavalry should absolutely dominate the battlefield if present in any quantity. This is often a matter of making sure that any RCW battlefield has low troop density, rather than rules though.
Bad RCW cavalry, and quite a lot of it was bad, was awful – far worse than the WWI equivalents.
Much of the time the sides had no idea where the enemy was, other than in general terms. Indeed much of the time they were quite uncertain where their own side was – it was not unusual for battalions to be out of touch with their regimental command for days on end. In such a situation scouting became key.
However, operational security was still poor, because many of the scouts were in short supply and untrained, yet had to cover all 360° around the unit. On top of this sentry positions were poorly maintained. Units were perpetually being surprised, both in the field and in billets.
With porous front lines, gaps 20 km wide with no troops in them were not uncommon, it was a simple matter to penetrate behind enemy lines. The result was units would often conduct raids deep into enemy territory – with anything from a company to a corps. Budënny rode around behind the Polish front lines for months on end.
Then there is the use of tachankas and armoured trains, which always need bolting on to WWI rules.
Support arms tended to be absent. Infantry rarely had mortars, and almost never flame-throwers etc, no matter what their official orders of battle say. Heavy artillery struggled to keep up with the pace of movement of the fronts. Tanks even more so.
Generally only ammunition came from the rear. The rest was largely foraged on the go. Supply lines could not wander too far from rail lines, as transport would not reach units in time. If they were fighting very heavily the units could not get food, and often went without for days.
Even sticking to rail lines, the dire state of the railways, with a shortage of coal (and what there was to sent to the armoured trains first) meant that troops often ran out of ammunition.
Poor supply lines and manouevre war led to the units having enormous trains of wagons following them, and the units had to be careful to guard them. Despite that, the number of instances of units having their wagons either destroyed or driven off is astonishing.
Some of 1914 was open and there were some assaults in the RCW that resembled WWI, so there are situations which cross over, but they were very much not the norm.
Since, for most of us, the charm of the RCW is that it gets away from the slog against trench lines of WWI, it makes sense to play games that do not replicate what caused that. Thus the rules need to emphasise movement and morale over firepower, and assume that most troops are incompetent.