The means of power for most of roman history (until around 867) simply isn't represented at all in CKII mechanics. In the republican period power derived from hereditary ownership of farming estates which gave you the money to pay for elections, public spending and personal armies. Factional politics within the Senate could help you put your money to good use but if you weren't quite wealthy you wouldn't be able to be a major player and you couldn't even be a senator without a million sestertes worth of farmland. This lasts into the early imperial era where imperial patronage becomes more and more important but land is still essential. Dynasties and dynastic prestige are important and the practice of adoption for heirless dynasties means that a dynasty isn't going to die out baring unusual circumstances, though it might diminish in importance. The gap in wealth and importance between the most important and lesser dynsties continues to widen throughout this period.
Once the empire starts to devolve into constant civil wars in the 3rd century and onward it devolves into a game of money and popularity with the army. Landed estates are still a source of money but they aren't so good as the population decline and taxation changes means they aren't as good as moneymakers and the exploitation of the proto-serfs and later serfs hardly makes one popular. The lack of Pax Romana means that it's far easier for a dynasties fortunes to widely swing between dynasties.
Into the fifth century things take two different courses in the east and west. The west is collapsing so power derives from your ability to get a gathering of loyal soldiers, probably from outside the empire and probably through dynastic ties to a powerful barbarian kingdom. The east is however still going strong so power derives from working your way up the ranks of the army because the army controls the wealth of the various parts of the empire as well as the troops necessary to win either a foreign engagement or a civil war. Barbarian alliances can help in the east but they aren't absolutely essential like in the west.
The west of course stops having politics after the fall of the west. However it can be noted that military leadership and land ownership were both useful for a roman dynasty that survived the fall and went on to marry into the new barbarian nobility the set up new kingdoms in Gaul and Hispania. The east survives as we all know and power starts to be regulated to the provinces where success in a good appointment is the route to political importance. Hereditary land holdings continue to be an important route to wealth and the decline in trade from the height of the empire means that land is back to it's place of primacy as a source of wealth. This lasts into the timeframe of CKII where imperial appointment (sometimes hereditary) and land wealth continue to be important but support from the church, the public and barbarian mercenaries all prove to be useful in staging coups or solidifying a regime.
So most of this is outside the scope of the game:
-Farm estate income (not in)
-Senate factions (not in)
-Barbarian alliances during the 4th century (sort of possible I guess if things were tweaked)
-Imperial patronage (not in because the player or AI favors whoever they please)
-Cushy army appointments (not in, no thematic armies to lead although you could maybe squint at the duke appointments and say that's what these are)
-Late Eastern non-hereditary rule (not in)
-Late Eastern hereditary rule (everything is shown this way)
-Support of the populace, church and mercenaries (no in)
Now I'm sure that some other more educated commentator is going to come along and say I know nothing about the political economy of Rome XD