Transcoding video won't work on a Raspi (in any realistic sense), and video streaming is pretty I/O intensive if you have multiple clients.
You can certainly get a similar thing working on a Raspi, but you'll likely notice buffering issues. Especially if you try to stream different content to different clients.
You can certainly get a similar thing working on a Raspi, but you'll likely notice buffering issues. Especially if you try to stream different content to different clients.