I remember the same "conversation" (read: flame war) in Game Jolt, and we basically came to the same conclusions....
"I think video comments are good if the videos actually show the game."
I must agree with leafo on that one (and no I'm not trying to score points with an administrator). There are not many ways in which a YouTuber can make the dev of a game know they shot that video, and loads of people will actually be interested if it handles videos about the game, whether it be "Let's plays", walkthroughs or reviews, or just videos showing a few playing techniques. Should all be allowed. When people do indeed shamelessly promote their channels regardless of being related to the game, I too think they are spam.
Now on Game Jolt I've seen a side problem in this discussion though. Some people branded YouTubers who posted RELATED videos to games as spam went shouting and using abusive language towards the YouTuber to vent their views on that. I don't know how that goes here on itch.io, but I think it should be taken a look at if that happens here or not.
Banning video posts from comments is not gonna solve matter though, and is in fact a very bad idea. For starters, I've already received some videos in comment sections on games I posted (not on itch, but on other sites) where the videos showed some very nasty bugs, and it was only to those videos I could see why they happened and come to a fix. Furthermore, especially when videos contain "Let's plays" or reviews, the videos do add information to potential players about the game, which can help them decide if this is the game for them or not, particularly since itch.io also allows selling stuff, such videos can then be of vital importance.... And I don't think dev approval is gonna work. Some devs never mind the comment sections of their game, and considering the time you sometimes need to put up a good video, it can scare serious video posters away, making everyone to suffer.
Best way to go is... Is the video related, leave it be. You don't HAVE to watch them. If it's pure channel promotion, report them, and let the moderators handle them.