"Is this person a/the leader of a government?" is probably the best guideline when it comes to this capstone. The type of government doesn't really matter; it just needs to be an organization dedicated to governing people. The mayor of a town, the queen of a castle, and elected officials of the Republic would all qualify.
You don't necessarily need to be speaking with the absolute top of whatever hierarchy exists to get the bonuses. Actions that don't involve speaking with a specific person such as "I incite a revolution" or "I provide support for X political party" count as "interacting with political systems" so long as the political system is indeed what you are interacting with.
Generally speaking, schools, universities, religious organizations, gangs, and merchant-guilds don't apply. Those organizations may have some kind of structure to them, but their core premises usually aren't about governing people directly. Groups of people that just sort of live in peaceful anarchy also don't apply.
Here are some examples, using some factions that you guys know about in play (this is not an exhaustive list):
Applies: Lost Legion, Republic, Second Empire, Principalities, Sardonios/Deturas, Davish/Wrothac
Does not apply: War Dogs, Tech Cult, Trailseekers, Limelight, SEED, Church of the Father, most CvI gangs, Moderation Congregation
We understand that the language used for this capstone was a bit unclear, so we plan to clarify it during the mid year update in a couple of months. I hope this helps. Thanks for asking; it has helped us clarify what we want this capstone to be!