Appeals Committee. Disputed situations in tournaments.

Then explain, on what grounds would he appeal the technical support decision by going down?

The idea is that in this case, the AK would not doubt the decision and would immediately issue a technical support ban to Dark. That is, the meaning of skd's sarcasm was precisely that Dark is now appealing (disputing the decision about) the replay, which you suggested to him. And there, he would be arguing with the technical support ban that the AK would issue to him without much thought. He would have no grounds, the joke was not about that.