Just ran across this article on a pneumatic CPU (8-bit only; tie not included).
Looking at this, though, I had to wonder if they looked at the targeting computers on the USS Iowa-class battleships. I think those ran on water, rather than air, but they had to be pretty similar. And what I remember reading about them at the time (this was late-80s) was that the only advantage there would have been to switching to a digital computer was greater available space. And they weren't exactly pressed for space.