Typically, Twitch videos (including this one) are served as HTML5 video content now, not Flash. 

The rendering problem itself looks like it's related to hardware graphics acceleration, and you would most likely need a driver update in order to correct it.  If one is not available, you might want to report the bug to your graphics chipset vendor.

You can determine whether or not hardware graphics acceleration is in play, by disabling hardware graphics support in your browser.

Here's a quick video on how to do it:

How To Disable Hardware Acceleration In Google Chrome? - YouTube

I am not able to reproduce. I tested the same URL as in your screeshot (https://www.twitch.tv/videos/145841174) On Windows 10 (Version 1607 OS Build 14393.1198) with Chrome Version 58.0.3029.110 (64-bit) and the video did not display in split screen as depicted in your screenshot. If you're still able to produce provide the Windows 10 Version and OS Build, as well as Google Chrome version.