It is correct that the first model that will beat ARC-AGI will only be able to handle ARC-AGI tasks. However, the idea is that the architecture of that model should be able to be repurposed to arbitrary problems. That is what makes ARC-AGI a good compass towards AGI (unlike chess).

For instance, current top models use TTT, which is a completely general-purpose technique that provides the most significant boost to DL model's generalization power in recent memory.

The other category of approach that is working well is program synthesis -- if pushed to the extent that it could solve ARC-AGI, the same system could be redeployed to solve arbitrary programming tasks, as well as tasks isomorphic to programming (such as theorem proving).