Hello! It looks to be a simple box for a 9V battery with a switch, such as this one (note: I have not tried this particular product). Given that Thom only uses the Alesis Q25 for a few minutes at each gig, a single 9V battery in one of those boxes will last a long time.
Thom playing the Q25 in Atlanta, Georgia, 2017.04.01 (flagpole). In this picture, the small power switch on the battery box is visible.