The amount of friction a user goes through to start documenting their life is extremely low, and since the stories get deleted there's no real commitment to be an active vlogger. It's easy to see why Justin is so active on it.
It's a powerful platform that an entire generation uses, and it seems like the applicants will still go through formal interviews. So it's simply a way to bring attention to YC.
Would a YouTube video pitch 10 years ago be silly?
Would applying over email in 1995 be silly?
Maybe back then, but think about how applying to incubators is done now.
Maybe Snapchat will never reach the level of popularity of either of those, but it never hurts to experiment, because it's experimentation that turned YC into one of the top incubators.