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.
(Why do I use the word ass so often?)