Edited because I misread the question..
On youtube premium, you can. Its a paid subscription service.
This includes the downloads, apparently.
As far as I know, YouTube video plays, views, and downloads all get a certain royalty.
Therefore I dont think its copyright infringement, at least if you are a subscriber.
However, it might be. I mean, Idk for sure, but it may also just be a practical way to have a digital copy of music you have previously purchased on tape or cd.
In that case, its definitely not copyright infringement, since you paid for the music already.
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Edit:
Ok youre asking about video gane playthrough… well, really it is copyright infringement, but in this case, its not enforced, because its just good publicity.
Now, if someone made a very similar game, thats a different story.
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