It's up to the moderators/community of a game to decide what to do with runs with unavailable videos. Some can decide to keep the runs, but some can decide to reject those runs because they no longer have a "proof" for their time. Both methods are understandable, and certainly legit.

If you want to keep your runs on this site, but not on YouTube, you will have to upload the videos on another site, and then submit the runs again.