Bankruptcy is just you admitting to the court/gov you're not going to pay your creditors, and you're ready to face the legal consequence (like reconstruction).
They filed bankruptcy in Manhattan because they are not going to pay their creditors in the US. That's it.
I read the question as it implies Evergrande is not a "China's property giant", which it definitely is. But I might read it wrong. I'll edit out my condescending tone.
They filed in Manhattan in particular for very good reason - the venue is extremely good at huge, complex bankruptcies like this. It's non-trivial to unwind these financial obligations, and is really only done in NYC.
They filed bankruptcy in Manhattan because they are not going to pay their creditors in the US. That's it.