That's because it would more accurately be called pumpkin pie spice, since it's based on the spices that go into a pumpkin pie. I guess it's just too many words for the general public to comprehend.
Do they? They don't say they do on the outside of the bag. Admittedly, I didn't look at the ingredients.
Edit: Looks like dried pumpkin is an ingredient, but it's pretty far down the list. I'm guessing it's not going to be a big flavor enhancer for a dog since they don't exactly have sophisticated taste buds anyway.