There's always the ol' "HDMI from the PC to the TV" trick.
But really, I've heard the PS4's web browser works pretty well for watching Twitch streams. There's also the built-in Twitch stuff, but I think that's only for watching streams of PS4 games. I could be wrong.
I didn't even know there was a 360 app... I'll have to give it a shot. I would much prefer to just throw it up from my iPad but this sounds like it will work.