So this is a tricky subject. If it's YOUR recorded footage, then yes, you're allowed to make a game trailer (although technically speaking the game developer owns the game, and thus the footage, as Nintendo had gone down the route of claiming and striking gameplay videos in the past)
If you're making a video using other people's footage, or official footage, you run the risk of getting a copyright claim. Sometimes they allow it as "fair use" if it's transformative, using their footage in a way that changes and transforms it... BUT that's not always the case.
I did a review of a Jurassic World trailer, I was giving my opinions, and reviewing the footage in an analytical manner, but I still got a copyright claim for using Universal Studio footage.. So it's a tricky one and a bit of a gamble really.
WORST case senario, you might get a strike (but strikes are rare for copyright, it's generally just claims)
Best case senario, nothing happens. But more than likely the studio who owns the footage MIGHT claim the video.
You can do this method, it will help you get videos without rights
In theory that sounds like a great idea to search by creative commons, but you're also trusting that people uploading that footage actually have the rights. Great in theory, but in practice I wouldn't trust that, studios have a tendency to claim videos even if the footage is used in fair use situations.