A Twitch Weekly broadcast from 18th July is available to watch on demand. However, as spotted by Eurogamer, half the show is muted. The show is a chat show and was discussing the Twitch universe, the DotA 2 International 4 tournament, and the Evolution fighting game tournament.
Twitch’s copyright recognition process is being applied to videos on demand for the moment. The streaming site uses Audible Magic to scan VODs for music owned by Audible's clients. This includes both in-game music and music that streamers may have running in the background. The former could be problematic, as the murky area of licensing rears its ugly head.
Twitch said, "If you wish to include music in your VODs, please remember that you are responsible for clearing all such rights (this includes ambient music that may be playing in the background while you are broadcasting)."
If you needed any more hints that a Google/YouTube buyout is on the cards, this is a pretty good indicator.
Meanwhile, Twitch also announced changes to its On Demand service. If you want previous broadcasts saved, you will need to make a highlights package, which is now limited to two hours in length. Highlights will be saved indefinitely, while full broadcasts will not.