I think I just found the reason why Biden's not running. This video among others wold be exploited by GOP candidates or Dm primary challengers. Candidates like Trump may not win the feminist vote, but he or a more likely GOP candidate could use videos like this to decrease voter confidence in the democratic party, reducing the gap if not eliminating it.
Besides, Biden wouldn't want his character to be tarnished in old age by exposing himself to attacks from rivals. That's why I think he's unlikely to run.