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.
The Soviet Union won the "space race" of course (or perhaps Germany did if you define it as suborbital space flight), it just lost the "man on the moon race". In any case, after losing the man on the moon race, the Soviet Union did not just dismantle their space program and focus on Earth. They continued to invest a great deal in their civil, scientific, and military space capabilities after 1969.
Will the Chinese Communist Party similarly collapse in the 2050s? Perhaps not, but they will be going through significant demographic decline from the 2030s; they are increasingly in conflict with the west and with their territorial neighbors; they may become involved in significant military conflicts (e.g., over Taiwan); their current leader has consolidated power and succession could be spicy. So who knows? It's not inconceivable. China would surely continue and continue a space program as Russia has.