That's pretty much what happens if you're running multiplayer through a third-party server, except that instead of sending video data, it's sending you game input and having you render the video locally.

But that's just the difference between downloading a starcraft replay file and watching it in starcraft, versus downloading a video of a starcraft game and watching it in a video player. One is a compressed video, and the other is also a compressed video, but with a different compression scheme.