Thís refers to thế animal, nốt thế meat?
This sentence translates to "I like chicken [meat] dishes". Món is a prepared food item/dish.
It's kinda implied that it's the meat of a chicken. If you wanna say "I like chickens" you'd use "con gà". :)
i wrote "i like chicken dishes". I feel like this should be correct, and even more so than "i like chicken dish".