Remember, USA won the Moon race by running centrally-planned project with strong government leadership, while USSR lost Moon race by having Korolev, Chelomey and Yangel design bureaus competing with each other.

In this case we have SpaceX as a driving force and potentially NASA which provides much needed incentives - both to SpaceX (they won't reject the money) and others (so SpaceX knows it's not alone). Government is still critical, as there is little commercial gain to get in a short term from the Moon.

SpaceX has a couple of aces at hand - Starlink and potential for wide use of Starship near Earth. China companies don't have as much of commercial incentives - for them, government participation is even more critical.

And then ignoring the American capitalist company doing exactly that.

It seems like you misunderstood this part.

It was Senator Todd Young who expressed frustration that Senator Cantwell piggybacked the unrelated amendment to the bill that is meant to help with "out-competing, out-innovating [and] outgrowing communist China" (<- this is by Mr. Young).