The circle just indicates the cooldown time for the Pod Program (big laser).One thing he was doing did leave me with a question, though. I haven't played the demo yet (will tomorrow or so I hope) so I don't know if it does anything, but I noticed that when he was using the pod's gun a circle seemed to deplete (or something), did that actually impact anything? Because it didn't seem to do anything even when he kept firing.
Regular shooting has no cooldown/ammo.
You can also turn off the cooldown display, along with other parts of the HUD, to make more room for upgrades (in the full game).