Usually the brightness keys should control the backlight and not interfere, but it sounds like they are doing something else.

You can try right-clicking on the desktop and choose "Intel Graphics Settings". Look in Power and see if any of the settings there make a difference. (Personally I always turn off dpst because I don't like how it looks).

There is also a slightly newer driver for the Intel 620, not sure if that would help or not:
https://downloadcenter.intel.com/product/96551/Intel-HD-Graphics-620

Expanding on this, I'd like this feature too as F.lux can be somewhat intrusive when playing videogames.

I think it would be an idea to have the software's features configurable to be toggled to be on or off or to have unique adjustments when you use fullscreen programs or just apps in general.