I haven't entered one myself, but I did get to be a tester once. One of our local animal shelters has a chili cookoff each year, and one year, my family and I went and voted on our favorite chilis. It was a fun time, and we got to taste so many delicious chilis!
Although I have had some good chicken chili ... if I were judging a chili cook-off, I would expect beef in the chili. That does not preclude the inclusion of other meats as well as the beef - but, for me, beef would need to be the dominant meat. Ground, cubed, chopped - not so important which way it is cut, as long as it is beef.
But, that is me - I also like beans in my chili ... I am not from Texas