This is a kind of pedantic take… Yes, they’re professionals competing in combat sports, the sole purpose of which is to fight in a controlled environment, so that you can determine a winner with as few deaths and grievous injuries as possible.

If we’re talking about MMA, then it’s literally a combat sport that was designed with the intent of settling the discussion of “which martial artist would win in a fight”, hence why pretty much all techniques are permitted (of course there are exceptions if you want to nitpick).

You can’t look at a sport where people are intentionally knocked/choked unconscious or have bones broken by opponents and say “they’re not fighting because there’s points and they get paid”. Professional combat sports is the closest we’ll get to modern gladiators.