I'm only a naturalized Texan of 26 years, but I have seen prize winning chili both with and without beans. Granted there are heated arguments here about the subject, with the "no beans" crowd being usually the most heated.
In mine, the beans (canned) are added next to last after boiling an hour in slightly salted water. Worse yet, they're half pintos and half kidney beans.
The Cincinnatti "chili" seems more like spaghetti sauce with beans than an actual chili.