It's actually AI's new PCP air rifle in that picture, and he's recharging the air cylinder after the pressure dropped too low after the last shot string. However, in keeping with British tradition when it comes to electrical component reliability, the AI branded UK built air pump that comes with the rifle already let the magic smoke out, so he had to replace the UK air pump with the Ryobi.
On a more serious note, he's just using the Ryobi inflator as a barrel cooler. I do something similar but use a compact rechargeable air mattress inflator. It's much smaller than the Ryobi but cranks out way more air than a chamber chiller or riflekuhl, runs about 40 minutes on a charge. I also don't like the possibility of forcing dirty air down my barrel if say a big cloud of dust gets kicked up and sucked into the inflator inlet, so I use a CPAP filter inline with the hose. Works quite well on hot days, but obviously not as well as a cool damp towel wrapped around the barrel.