I feel that he doesn't want to come into the house because he doesn't want to deal with you face to face - either because he thinks you'll kick off/ be sad at him, OR because he's actually feeling so bad about moving out that he thinks he'll lose the strength to go back to GF's once he's in your house again.
Personally I think it's probably the first rather than the latter, but who knows.
I agree that you should not facilitate this behaviour though. Tell him that, if he wants his stuff, then he must come in and collect it himself, you won't be doing it.
Part of the reason you shouldn't do it is because it will also feed into his narrative that you want him gone - which of course you don't - but he could take it as confirmation that you do.
Another part is that he's decided he wants to be independent of you, so why should you do his dirty work for him? Let him do it himself.
Hopefully he'll choose to come and talk to you at the game tomorrow, but even if he doesn't, he'll have seen that you came, and he'll know that you still care and support him.