The games were everywhere. They were (and mostly still are) said to have Etruscan origins. There’s an Etruscan tomb painting showing a mostly naked man, unable to see because of the bag tied over his head, trying to defend himself against a brace of vicious dogs. Now *that’s* entertainment. The Etruscans had these things as part of their funerary rites, and early on (late republic, early empire) these types of combat were indeed held in honor of eminent people who had died. The arena was called the spectaculum (or somethin’ similar) and the spectacles held there were quite varied (acts we’d associate with circuses; parades of exotic animals; parades of exotic human captives) until the death by combat thing became so popular. Politicians would underwrite games just to get themselves known and liked enough to win office.
You could make a good case that modern Hollywood has revived the fight to the death games. It’s just done today with special effects.