Sure; but you can train one agent/hero so the training scales in a somewhat linear fashion once they get beyond ~15-20 heros. The computer won't be able to nail the full complexity of the game - but neither can a human, and the evidence from Go is the amount of the game a computer can grasp is much greater than a human.
Humans can't fully understand full DotA either; it is common for pros to be surprised by mechanical interactions or quirks on specific heros.
It might be an interesting theoretical challenge, but there would need to be some solid evidence of that beyond OpenAI calling it done and going home. Especially given the breakneck speed that the first 17 heros got trained. The AI was improving faster than a human does in MMR/day rates for specific heros. It looks like they got bored once the outcome became clear but needed a lot o work to achieve.
> If this was a task in the real world, the AI would have the same interface as humans: The screen.
This part of your argument is weak; you are relying on a computer having human limitations to show that it is superior. Computers don't have human limitations; that is a significant part of why humans can't compete with computers.
> I think for AI to be able to claim that it is better at a game than humans, the AI ought to be playing the actual game, and use the same interface.
What could you do if the bot people don't agree with you? When TeamDotaBot2000 is winning every game on the DotA ladder you can write them an angry all-chat message saying they didn't really win while your hero dead and their destroying your tree. That'd blend right in with the usual DotA crowd.
> You might think that would be a trivial and useless exercise (like it would be in Chess/Go), but I'm really not convinced of that for video games...
It isn't trivial; but it also isn't hard. It is time consuming and there are a lot of practical things that need to be solved. But if the resources are spent, it is expected that computers beat humans in any field with formally defined rules and objectives. That is a big deal.