Thank you for this response, however it isn't helpful. All gameplay is copyright by its very nature; it's just that the games companies choose not to enforce that right on YouTube as it is in their interests to see the gameplay circulated (for promo purposes).
My question is: does Udemy prohibit the inclusion of gameplay in the videos you upload?
I can find copyright free gameplay on youtube. However, this is not the answer you are looking for. I thought you wanted to use gameplay as a background for your videos.
Udemy doesn't prohibit such content, as long as it is yours. However, if the game company makes any claim, then udemy cannot help you.
From a legal perspective, you infringe copyright in specific cases only. For instance, if you use game music as your video background music then you are infringing the copyright so you cannot do that. If the music is played in the context of you talking about that music and its authors and the game where it's used in, then it falls in the fair use policy, hence you can do it. Basically, as a rule of thumb, you can say that as long as you are showing a game usage and its music to the end of talking about it, it's ok. If the game footage or music is used as part of your own production (background, intro and so on), then you cannot do that. You can find a lot of literature on this subject, just google "copyright fair use".
Udemy enforces this rule strictly.
It would be best to write firstname.lastname@example.org and ask them.
I suspect their stance is that it's up to you to stay within the bounds of copyright law, and they simply follow DMCA guidelines should the copyright owner file a takedown notice. It seems like you're in a gray area as far as "fair use" goes and you'd be best off asking a lawyer if you're concerned about it.