@suchtla I couldn't find any rules for it, but I did find that arm wrestling is listed as a "sumo sport" in the japanese wikipedia - which I found interesting enough to share.
(So basically he's dragged into and loses a game of arm sumo, and then he suggests push sumo as a pretty close follow-up, since they are both sumo games)
The rules are pretty clear from the comic though.
The players face each others, tries to push each others over, but the first one to move their feet loses. (So if you try to rebalance by taking a step back, you lose, or if you advance on your opponent to push them more). And to make it easier to tell, if your opponent falls over you, clearly they overextended and they lose.
(Like main sumo - only open hand palm strikes. And no hooking/pulling.)