If we beat the Chinese somehow, I don't think they'll just dismantle their space program and focus on Earth. They'll keep going, and they have the economic base to expand their program.
I think we're seeing the beginning of a new kind of space race. It's likely to be much longer term and grander in scale over time, as we compete for the best spots on the Moon and the first human landing on Mars in the decades to come.
However they have their own timetable and milestones , hence going to the moon has already been earmarked with followup misson for a lunar base and further missions already penned in. So less of a race if one party is just doing their own thing.
We see the same dynamic viz Taiwan , western commentariat seeks to impose deadlines and spin rationales when they never materialise. Or the AI race where China keeps churning out OSS models while American labs are in a sel declared 'race' for supremacy.