The EC decides what the rules for defining a gatekeeper are, they invented the designation. You can call that arbitrary if you want, but they set their rules and are sticking to them. Deciding that iPads and iPhones are the same platform seems pretty common-sense to me.
> The EC decides what the rules for defining a gatekeeper are, they invented the designation.
It's more complicated than this: the EC has the initiative for legislation in the EU but the text they submit is later amended and voted by both the European Parliament and the Council (representing member states) so it's not true that the EC defines the rules. And both the member states and the European Parliament are pretty jealous of their prerogatives in the decision process so you can be sure that the EC cannot have arbitrary power that bypasses the Council and the Parliament.
If the unqualified existence of judicial remedy justified any arbitrary bureaucratic action, the world would be a much worse place (and indeed countries where bureaucrats make up rules to suit their whims and your only recourse is the judiciary tend to be dysfunctional).
You are making things up: there is no arbitrary action at all here. The EC must abide to the DMA and have no power to overcome it. If they did it would basically be a coup from the Commission against the Parliament and the Council, and you can be sure that member states would not stay silent against it (but don't worry it's not going to happen, as the balance of power is clearly not in favor of the Commission).
I'm just using the CJEU as an illustration that Apple themselves doesn't believe in the “arbitrary rules” narrative as they aren't even fighting in court.
Also, you're trying to use the “bureaucrates” card here, but Apple executives are bureaucrates too, and Apple's management of sanctions and their habits of shutting down user accounts without recourse shows that their own bureaucracy is closer to the one from authoritarian regimes than anything else.
I believe it follows the Digital Markets Act (DMA), a European Union legislation designed to promote fairness and competition in digital markets. You can find more information here: https://digital-markets-act.ec.europa.eu/index_en
There are no rules that are governing what is or isn't a gatekeeper. It's just whatever EC decides that day.