They invited him because they were introducing a private economy and figured that a capitalist economist would be able to help them do that, but they didn't take his advice and remain hostile to actual neoliberal economics.

It makes sense to rely on liberal economists for advice when liberalizing an economy, since that's their expertise, but it's innacurate to call Chinese policy neoliberal given how enormous the state-owned sector of their economy is. You very notably don't see the policies of neoliberal Chile being implemented in China. Where are the privatized roads?

Again, what evidence do you see of an impending takeover of the CPC by neoliberals? Liberal economic advisors in the government? These people aren't even in the party.