"What would happen if i put a trade mark on the word kickboxing or karate ?"

You would be denied that trademark because those are generic terms.

Coca-cola doesn't have a trademark on the word "cola", so they couldn't sue anyone for using that word. Pepsi is short for Pepsi-cola. There are lots of other generic "cola" brands. "Cola" is in the free-domain, much like the words "milk", "cheese" and "bread".

K-1 was a brand name created by the K-1 corp. The value and meaning of "K-1" was built up by them, after millions of dollars of investment over 15+ years. "K-1" meant nothing in the fight world before they established its meaning. They did all of the work with brand development.

Any one of these other promoters that do fights with similar rules to K-1....they can develop their own brand too. In the MMA world, there is M-1.