I'm mistrustful of all sides of these discussions where people argue that people are making things too political or that everything is politics or related to politics or whatever. The whole way it is discussed seems to misplace the actual grievances and leave the whole discussion intractable. 'Politics' is a pretty vague term and most things can be loosely related to politics in some way. The people who complain about injecting politics into games (or whatever else) are often just unwilling to see the obvious politics in a situation, but the counter that everything is always political anyway seems way too general and vague, and just unconvincing. If everything was politics, why do we have the word. Certainly it is meant to mark out something non-trivial which can be lacking or at least present to a lesser degree or just less relevant in certain discussions. Something related to power-relations and policy and the organisation of society.
On the one hand, if people want to discuss politics in relation to something else, let them. Politics is probably relevant in some way, and if you personally don't care, go do something else then inject yourself in the discussion just to say you don't care. Jim Sterling can discuss whatever the hell he wants on his show on his own youtube channel. And in the case of videogames, the way they are made, the way they are funded, the way they present characters and situations and all that is often very political. We are dealing with questions of labor rights, representation/acknowledgement of minorities, consumer rights, the formulation of gambling laws, representations of war and the place of existing countries in it and so on and so forth. Those subjects are obviously political.
On the other hand, the idea that everything is politics strikes me a bit like the idea that everything is chemistry. True, in a way, but the chemical or political aspects of a thing aren't always the most relevant and I've absolutely seen people try to put square pegs in round holes by trying to interpret politics (often very specific politics) into something where it just doesn't work that well. I'm always a fan of analyzing things, especially art, on their own terms first, and sometimes I get the sense that some people have lost the capacity to look at things from any but very specific perspectives. I remember that Bob Chipman tried to argue that halo represented diversity as bad because the one-species UNSC fought the diverse covenant. Thing is, I'm fairly sure the covenant were designed for gameplay purposes first. Analyzing their presence as a political statement just isn't that convincing. In addition, in halo canon the diversity of the covenant is the result of imperialism and domination by the elites and the prophets, not of peaceful co-existence. The analysis itself is wrong, and I don't think it is crazy to suggest that it is the result of somebody applying a certain politics lazily to a series of videogames they didn't really like or understood the appeal of in the first place.
I think my take is that there are definitely people who read politics into things where they probably shouldn't or where it is clear that they don't understand the specifics of what they are talking about and approach the thing instead through pre-conceived politics. That being said, the criticism of inserting politics into everything is way overused. This has resulted in an all purpose counter that 'everything is politics' which imo is too trivializing and glib.