If I want to upload a game to speedrun.com, can the video I have to upload belong to someone else or does it have to be mine

To request a new leaderboard, the video must be your own gameplay.

In the additional notes section, you can include links to videos of other people's runs in order to show that people are interested in running the game, which might increase the odds of it getting accepted. But if you want to fill out a game request, you do need to have a video of a run that you yourself did.