I was checking the leaderboards with regards to where the runs start. Turns out the videos to some aren't available anymore, regardless whether they're from Twitch or YouTube.

Should these runs stay on the boards for legacy sake, or taken down? I have verified (most of) them previously, but are they still viable if there's no proof, especially if they rank 1st?

I think they are. If they were verified, and the video was lost, then it still means that runs were done at some point with proof.

Even if we wanted to make a rule against runs with lost videos in the future, lex retro non agit. No matter the circumstances runs done earlier should be respected.

It'll bug me, but noted.