That's an interesting insight. I had not thought about the possibility of a scientific understanding of pressure developing prior to the steam engine. If you have some pointers to read up on this, I'd love to learn more.
Also, there were demands for pumps in antiquity, particularly in hydraulics. Lot's of labor was invested in building aqueducts and underground waterways. I always saw the Aeolipile as a tech demo showing that heat can be used as a power source for mechanical motion, but this is probably because I live after the steam machine, knowing it's true potential. I've long wondered why the idea wasn't expanded upon by the Romans or later the Greeks or Egyptians, but I suppose it wasn't convincing enough on its own.