Chicken tempura usually means the chicken is battered in flour before frying and then accompanied with sauces, such as soy sauce or salt. What you might be thinking of when thinking about Japanese fried chicken is karaage, which is usually marinated in a mixture of seasoning before being battered and fried.
I think the tempura is the batter and the technique to making the batter itself instead of the inside, but the mosy well known outside of Japan is shrimp tempura. As this manga has shown me they have seasonal tempura, mix veg, mushroom, seafood, meat, etc. But they’re all still called tempura albeit with an additional name to classify what type.
Tldr: as long as they’re that light, crispy coating made from tempura batter, anything is tempura
YOU CAN MAKE TEMPURA OUT OF CHICKEN!?