I kinda agree with a lot of what you said so I won't address that, but about that EC episode...
bartholen said:
At 20:07 he says we can relate to this gay character despite his sexuality, which to me kind of debunks the whole "we need more inclusion in games" thing. I mean, the title of the video is "Why a gay character made Persona 4 great", implying that the character made the game great BECAUSE they're gay. Which is horseshit. It's not about the character's sexuality, gender, or whatever the fuck. It's about whether or not they're a relatable and interesting character.
I think you're looking at this the wrong way. There's a difference between being able to relate to a character and having certain groups of people represented in media. Take a game like Thief for example. I'm not a thief like Garret is, I don't find myself constantly evading law enforcement to do my job. Yet I can relate to his non-partisian stance, being confronted by two extremes and choosing neither. I think a lot of us can relate to that.
I'm sure gay people can relate perfectly well to straight characters, but does that mean we should have nothing but straight characters? Having relatable gay characters can open up new gameplay experiences, as well as explore themes that haven't already been done to death with heterosexual themes. Also there's a difference between "a gay character made a game great" and "this game is great specifically because it has a character that is gay". The latter suggests that just the fact that there was a gay character was enough to make the game great, while the former suggests that a character that happens to be gay made a game great.
Now I know a common response to this would be "but why does it matter if they're gay or not?" Well it's because gay characters in video games are so rare. Having a gay person be the breakout character in a video game is quite remarkable, so Extra Credits y'know... remarked on it.