Quick question if anyone can help:

I am planning to do a speed run on Wii for this game but don't have a capture card to get video of it through the Wii. Would I be allowed to use an external camera and have it focus on the television screen? That is the only way I can think of to do so. I will have my splits ready and everything overlay-ed to a video through OBS, but the camera is just the one stipulation I am worried about to qualify. Thanks!

Yes, that is fine.