Since in the rules it says that bandicam or something along those lines is required. but is it allowed to use Geforce experience Fps counter instead?

Bandicam is just an example, you can use whatever you want as long as it displays the fps the game itself is running in.

You can use, Steam Overlay, Dxtory, Rivatuner. MSi Afterburner with Rivatuner. Or, Fraps. Or, anything else that displays the FPS Counter. I would prefer Steam Overlay. Or, Rivatuner. But, If, you don't want to download the other programs That is totally up to you and your personal reference. But, which ever Application is more reliable for you. I accept that. I would prefer in my opinion Steam Overlay. Or, Rivatuner.