For uploading a run, does it have to be to Youtube or can it be to another site as long as the mods have acess to view the speerun in its entirety? (such as Vimeo or DTube)

Highly recommended to upload to YouTube. You can upload to other websites, but it might take a significantly longer time to verify depending on the website.

Also, the retime may not be as accurate due to lack of tools for websites other than Youtube.