Well, here is a little more information about the different factions with Red Dust Revolution, and a bit about how they interact with each other. (Click on images for bigger versions)
Very quickly you may note that the core actions for the MG player do not diverge hugely from a normal COIN game. As i've said before, this game is not a radical departure in terms of mechanics.
What is a little different is Bombardment. Which is a modified Air Strike. Air Strikes against domes would be considered an atrocity, so, while they remain an option for the MG player, they come at a cost of support back home.
Another unusual ability if Contract, which trades resources to the CORP to do a combined attack. As the CORP is loathe to do any real fighting without clear profit, it is a way you can force you "ally" to play a team game.
Eradicate also gives the MG player incentive to hit the wastelands and to try and dig out insurgent bases.
The CORP has the same abilities, but Train works a little differently. Unlike many COINs, the local government forces aren't trained by their ally, but there also aren't desertion mechanics.
The CORP can also train black-ops teams, which are nasty little units that can remain hidden and hit like insurgents using the Raid special ability.
The CORP controls much of the infrastructure on Mars and, as a result, has Shuttle, which can be used to massively reorganize the board. This is the most efficient way to redeploy and reinforce areas, and can be used for great good, or ill.
Exploit drives the CORP player, and allows them to pay off any faction, or line their own pockets. As profits are the factions path to victory, they really want to set up shop and combine PR efforts (under train) with exploitation to drive up profits for the win.
Again, very normal looking actions for Free Mars, and in many ways they play like the Taliban or VC.
Rally, March, attack and terror are very typical COIN abilities.
Redistribute allows you to take resources you need to power your factions.
Defection allows you to take control of units in regions, as their loyalty to mars outweighs their loyalty to a pay cheque.
And finally, Ambush is as it always has been.
Free Mars is very much a "no surprises" faction for veteran COIN players. Although, because of the nature of the board, and where population centers are, they are heavily focused during games on the major domes.
The Reclaimer Church
Now this one gets a little more "out of the box". While the abilities are pretty normal (asides from Rally working as well in 0 pop regions as 1 pop), Ransack is something quite different.
Ransack can reduce a domes population by 1 and create a refugee +1 population marker that either the Free Mars or Mars Government player can rehouse. It also generates considerable resources.
However, if a dust storm occurs (the "break card" of Red Mars revolution, like Monsoon in "Fire on the lake"), those refugees die, and that population is lost, permanently.
Less population makes it harder for every other faction to win.
This power is a "nuclear option" that gives the RC incentive to attack domes, and makes sure that all other players treat them with some respect. For while they are mostly content with building their wilderness network, when they mass to attack, it can be devastating.
Preach also allows the RC player to subtly manipulate the balance of power. (note, reference card says FM insurgent, that should be RC, these are slightly old versions)