I'm actually not certain that this is true. Normally I would agree, but it is specifically a question about gaming content. If we follow the logic that gamers require the permission of the developer in order to post content that isn't applicable under fair use, then the logic flows in the direction of all game footage of a game belonging to the developer regardless of who captured it. Under that scenario, so long as the uploader doesn't include the voice of the source channel, then uploading video game footage captured by someone else applies under the same permission license granted by the developer in the first place.
The question of who does the footage belong to is a difficult one, but I don't see any court siding with the YouTuber on this myself.