Completely forgot about the kiss scene. It's been forever since I've seen it. But yeah, that's definitely/obviously George's climax. So let me amend my answer a bit...
To keep using The Matrix comparison, Neo finally believing in himself in the subway, right before he decides not to run and instead face off against Agent Smith directly ("He's beginning to believe"), is the equivalent of George finally punching Biff. It's the moment the hero is finally able to embrace the lessons learned and realize his or her Inner Need. But the embrace isn't quite enough. The hero must then apply/act on that new-found belief to achieve his or her Exterior Goal. So, Neo finally stopping the bullets is the culmination of that decision realized in-full to achieve the External Goal (defeating Agent Smith / becoming The One). Similarly, George now has the bravado to earn Lorraine's love, but he needs to apply that newfound bravado, or it's all for naught. So once he realizes his Inner Need (to man up) he can finally achieve his External Goal (win over Lorraine), but he must do so with a kiss (the act that cements the relationship). I had forgotten about his pining after Lorraine throughout the movie. For all intents and purposes, the climax begins when the hero finally embraces the lessons learned/their Inner Need, and ends ends when the hero applies those lessons learned/Inner Need to achieve their External Goal. So, yes, punch-to-kiss, for George, is HIS climax, which happens to brilliantly overlap with/directly affect Marty not being erased.
Again, it's been forever since I've seen it, but I'm wondering if Marty likely has an Inner Need as well (something he needs to learn), even if super subtle, before he can finally go back to the future at the clock tower. Maybe it has to do with not being erased, or maybe it has to do with the whole "chicken" thing, as that obviously ties into George's plight as well. But Marty obviously then gets HIS climax at the clock tower.
Either way, it all hinges on the decision to make Marty the "guide" character going into act two. Again, that tweak is what gives the movie its two-pronged climax, because any other movie would essentially be over the moment George kisses Lorraine, as George and Marty would be one and the same/the sole protagonist.