So, my answer "She is eating chicken" was wrong. Is there a different way to refer to "chicken" as meat rather than "chicken" as an animal?
itheann sí doesn't mean "She is eating". Irish, like English, has a separate present progressive construction, tá sí ag ithe. The simple present and the present progressive (or continuous present) are not interchangeable, in English or in Irish, though other European languages don't always make this distinction.
The technical term for "chicken" as meat is circeoil, though sicín is commonly used for the meat too.