What purpose could baking soda and cream of tartar serve in a meatball recipe?
According to Cook's Illustrated's article Tenderizing Meat with Baking Soda (possible paywall):


  Briefly soaking meat in a solution of baking soda and water raises the pH on the meat’s surface, making it more difficult for the proteins to bond excessively, which keeps the meat tender and moist when it’s cooked. 


This is almost certainly the effect of the baking powder:  to help create a more tender product.   This is probably especially necessary given the lack of bread products (which provides starch that physically interferes with protein linking, and helps retain moisture in the, thus producing a more tender meatball).

The tartaric acid is probably there because recipe authors are used to pairing it with baking soda which is necessary when it is used to create leavening in baked goods.  In the meatballs, it will simply tend to help make them more acidic, although it will also neutralize some of the baking soda.

I have surveyed several recipes on the web which include baking soda in meatball recipes; they variously claim that it helps make the meatballs lighter or more tender.