Ok, looks like I was a bit off on the compressor angle. It wouldn't take running it in reverse, it just requires offsetting the valves (in purple) by 180 in the cycle. If you have a mechanism that can do that, then the engine can switch into "regenerative" mode mid-operation. That's got a bit of potential for vehicles with regenerative braking.
Just to elaborate a bit on that possible use case, let's imagine a relatively low speed vehicle that has a hybrid electro-pneumatic drive train. It's overall air storage capacity isn't huge, but it takes the acclerative power demand off of the electric system which is there to recharge the air tank and augment the engine through different power modes. Overall vehicle weight could be lower, and cost could probably be lower too, given less batteries.