What happens is that animatronic robots fight. It's sort of like watching super-stiff mixed martial arts guys swing away. To be blunt, the fights are comically clumsy, though some hydraulic fluid squirts around and there are lots of sparks.
You can watch the first episode here. Just skip to the 32nd minute or so and you'll miss a lot of padding. The entire episode only offers about three minutes of actual fighting, and eventually things fizzle out into a fluid-leaking TKO. Pretty anticlimactic, I'm afraid.
Let's face it, I'm not the target demo for this stuff. But if you're male and on the front side of thirty years old, you might enjoy the few minutes of actual combat. It's still hard to count Robot Combat League as a game show, though other game show sites are covering it. I'll just call it Popular Mechanics Sports Illustrated.