I think the cycle time on this would be far superior to a pneumatic system: cycling this system effectively means lifting ~100 pounds ~8 feet, which a reasonably fit person (who could reach that high) could do several times a minute for extended periods.
He got an efficiency over 40% (if memory serves, I watched this video yesterday) -- I wonder between pumping and discharge how efficient a pneumatic system would be, but I can't imagine that it's higher.
If the pump were operated by a bicyclist and the projectile feed automated I imagine the pneumatic system would win out by a very wide margin regardless of any reduction in overall efficiency.