Like title says, I thought it would be a required field to fill, but really the Time is like the only required field to fill.

It's up to moderator discretion when it comes to requiring videos. Games that aren't run very often generally don't require videos. Most leaderboards require videos for fast runs and don't require videos if the run isn't near the top of the leaderboard. Some leaderboards require videos for every run. The game moderators decide everything.