The thing is, China has local ownership controls, over investments in China.
Are there similar restrictions, on Chinese operations in Europe or America?
Since the Chinese firm was able to bid on the airport, I imagine that in Spain, the controls, if any, don't apply to partially-finished, abandoned airports. Given the many ways in which the Spanish government can stick it to them, regulation-wise, I'd say it's a risky venture and may well turn out to be a money pit. Still, the Chinese are nothing if not gamblers. We'll see how this venture pans out, soon enough.