that's the thing, it depends on how it's done. It's obvious that games will (and should) touch on political topics, it's only natural. The thing is that when it's done in a preachy, one-sided, void of nuance manner it becomes more of a propaganda piece and less of a game, more of a political statement than a story that is believable, intricate and relatable. Let me give you an example from Pathfinder tabletop I've heard being discussed about a year ago.
They decided to do away with all mentions of slavery in the game... because slavery is obviously bad... but it's literally a game in which "bad" is almost a necessity so that there can be a plot in the first place. So, in the name of advancing a political message (one that will hardly find anyone in opposition pretty much anywhere) they're willing to compromise the game. See what I'm saying?
Sorry if I'm not convinced, but I've seen that said by many people when challenged, but they rarely stick to it in practice.
In fact, the source of that video is a great example of the problem I have with "anti-woke" sentiment in general. Half of his videos are complaining about the existence of minorities, gay people and women in media being woke and pandering. He(and many others who express your sentiment) don't care if the characters are nuanced or believable. On the first page alone, there are 4 different videos about shows that aren't even out yet! How the heck could he know if the characters are well written?
Maybe you aren't as absurd as he is, but that doesn't really vibe with general sentiment I see from most people.
Actually, can you give me an example of a few shows or movies that is definitely not woke and handles characters well? I have a feeling they're more "woke" than you think.