There are other locations where pila is used for singular, too (like the selection list for a stockpile).
Actually, the game was written with the awareness that pila is the plural of pilum. Here's the in-game description: "Pila are spears for throwing. They take a long time to throw, and move slowly, but one hit can do heavy damage. The singular of pila is pilum."
The description conveys that it's a bundle of pila, not a single pilum.
I'll buy that logic.