The interface really matters. And, I think YouTube is a good example where it’s worth considering ways where the interface matters more than what we usually think of as the “video format.”
At this point, I think it’s less that people really want to watch videos than it’s that YouTube has become the universal play button of the web.
Think about how hard it is to reliably get a play button on the web, in general, and how much can go wrong, still, when trying to play something. Where do you find it? Where is it on the page? Is it going to work in my browser? Will it play or stutter? Is it the right size?
YouTube has solved all that–not that their solution is perfect and ultimate, but people trust it way more than other interfaces. It’s maybe more trustworthy than the web browser itself (you change between Firefox and Chrome, but YouTube is still the same…).
And, that trust carries over to non-web devices, where the expectation is that a YouTube app is going give you the familiar YouTube experience (e.g., on the iPhone).
I don’t think what happens inside the space of the YouTube player is so defining of the medium. People aren’t surprised seeing Hollywood trailers in the player, and they aren’t surprised seeing a single static image of an album cover, either. Those have basically nothing in common, other than that they corroborate that the YouTube player is the place to rest your eyes.
But, the player is the real thing that people can share. And, the web pages on the YouTube site are like the full version of the player / the embedded version is like a portable player. Home stereo / boom box.
And, to make a comparison, the YouTube player is to the wider population of the Internet something like what the UNIX command prompt was/is to those of us who started programming in the 1980s and/or making websites in the 1990s.
It’s where people really want to put their attention / cursor so they can prompt cool things happening.