"Half my chili is gone!" "Sorry, I ate it."

"it" in that construction means "half my chili". Just as in "My southern, three-day-cooked chili is gone", "it" is "(their) southern, three-day-cooked chili".

"This chili is no good!" "What's wrong with it, I ate (some of) it?"

The parenthetical is omitted but implied. Unless they're referring to the chili that is inside your digestive tract?