Well, the problem with that is the difference between "keep politics out" and "keep propaganda out" is kinda meaningless on its own. Because what is the difference between them?
Propaganda tries to force belief in something, and leaves no room for making up your own mind. It doesn't give you the evidence, it just demands that you believe. It tells you "this is what you should believe. Everything else is wrong. Trust me". For example, trying to show any nation as a wonderful perfect place without mention of the flaws. Kind of like how Tom Clancy books are all "America can do no wrong. Our enemies are just horrible people who love killing innocent civilians and hate Americans, specifically, but just trust us on that because we're not going to examine their motivations at all".
I actually felt insulted the last time I read a Tom Clancy book because of how little time they spent on the motivations of the antagonist. It was actually just the narrator saying "He was a fanatic. He hated Americans", and that was it. No explanation why. That's propaganda.
To include "politics" in a game would mean viewing an issue from multiple sides, where you can see why people might come to different beliefs about a subject. At the very least, it'd be a fair and nuanced criticism, as opposed to "this is just wrong". These are things that propaganda would never do.
For example, in a certain metal gear game, the antagonist is all about survival of the fittest. The cutscenes before, during, and after the fight are all about the guy explaining how he wants to create a war to burn America to the ground so that a new breed of stronger people can come out the other side. When the protagonist wins, the antagonist says "See? I was right. You were stronger, so your will gets to remain while mine dies off". So does that mean the antagonist is right? If he had carried out his plan, would it have worked out for the better? Since this was averted, would the problems of America continue to fester, like he had forseen? Those questions remain unanswered. It allows the player to make up their own mind. That's politics, as opposed to propaganda.
But you should check out his politics of Darksouls video, its really good and an interesting take.
I watched a bit of it, maybe up to the half-way point, and I think this actually supports my point. The choice to uphold the "status-quo" at the benefit of the ruling class (Gwyn and the gods) and to the detriment of your people "the age of man" is presented as just that. A choice. You could choose to either do it or not. The game doesn't try to force that there's one right answer. Giving the player a choice is a way to keep something from being "propaganda".
I mean when it came out that Tracer and Solder 76 were gay there was a lot of backlash from people wanting politics kept out of games.
I think when evaluating the inclusion of politics in games, one should think about whether or not the inclusion serves the narrative in any way. Does this inclusion matter? Does it enhance the narrative? Is it necessary to the plot? If it doesn't, it might be seen as an annoying attempt to shove a belief down a throat.
For these examples, no, I don't think it matters, nor does it enhance the narrative, nor is it necessary to the plot. If you didn't pay attention to the lore (that you have to watch youtube videos and read comics to understand), you'd have no clue. So why was it included?
Why did the Harry Potter author try to make one of the characters black, and another gay, years after the books had been written and the lore had been established? Same thing.
Bioshock 1 is a game with a very clear thesis statement; that Objectivism is fucking shit. The ideology of Rapture directly led to it's downfall as the hideous wealth inequality led to the civil war which collapsed the city.
Just because an ideology is criticized, it doesn't make it propaganda. The fact that you know what led to the downfall of Rapture is proof that this is good criticism. It's not just "This is what you should believe, just trust us, we won't bother going into why".
Like I said above, just now: Propaganda tries to force belief in something, and leaves no room for making up your own mind. It doesn't give you the evidence, it just demands that you believe. It tells you "this is what you should believe. Everything else is wrong. Trust me".
Then they should say what they mean (and mean what they say). Besides, what is the point of having a discussion on anything if everybody's forbidden from saying something someone else disagrees with? The whole "keep politics out"-argument overwhelmingly means "keep post-modern status quo criticism out" (as in feminism, GLBTQ and social justice).
So you refuse to give people the benefit of the doubt and rephrase "politics" to "propaganda", because "they should say what the mean and mean what they say"?
Fair enough, but then, instead of just taking people at their word and leaving it at "politics" you want to rephrase it to "post-modern status quo criticism"?
We can't have a discussion if we can't agree on the terms being used, and we really can't if we're redefining those terms to paint the "other side" in a bad light. That's like imposing a handicap.