I hope they add the ability to resize panels on watch.lolesports, because I like having chat, but the stats frame makes the game just a little too small.
Below the video on the right side there is an options menu. If you click that you can change your stats layout to Theater. This will move all of the stats below the video allowing you to have chat and video up top with stats below the video. Hopefully this gets you closer to the viewing experience you want.