How to turn off screen while on MHL?

Hi All.
I recently tried playing Asphalt 8 (with a gamepad) while on MHL connected to my TV.
(Phone is a 1080p Xperia Z ultra)

While it displays, the performance on TV is much slower than on the phone itself (which is perfect)
I imagine this is due to the GPU having to drive 2 displays at the same time.

While there is an app that reduced the backlight of the phone to 0 (an XDA developer)
https://play.google.com/store/apps/d....screenstandby

I don't think this will help with the performance.

Am I the only one with this problem? is there any way to fix it?
Nobody plays games on a TV?

thanks!