I'm surprised that Youtube doesn't have a concept of next/previous episode. Of course there are workarounds like video replies or playlists. Maybe they want to discourage splitting long videos (eg. movies) up in 15 minute segments to avoid the time limit for non-partners?
You could watch the
Power Supply Design playlist, although it's in reverse order for some reason. The second episode is actually linked from the description of the first video on Youtube, but the third and fourth are not. I guess it's a pain to go back to the previous episode and add the link.
As for watching from eevblog.com, it's just embedding Youtube, so I'm not sure if Dave should spend the time trying to make it more like Youtube.