Because I don't expect a video player to rape my CPU so hard. It's ridiculous that a 720p twitch stream takes multiple times more CPU power than playing a full 3-D game. It's just frustrating that Twitch hasn't followed through on their promise for a html5 player.
What's interesting is that if I watch in the inbuilt steam browser instead there is no performance impact that I can see, which is super weird, since it doesn't seem to matter if I use chrome, firefox, IE or edge. Maybe it's just something in my system freaking out over playing video on a 2nd monitor with the main screen occupied in a fullscreen game.