In this scenario, "making its way over to..." is a way to say that something successfully got from the place it was created to a new place. In this case, people decided the opera written in Asia would be popular in NYC, so they went through (or are going through) the process of getting the rights and/or cast to preform it in NYC. In a more general sense, "(something) making its way to (somewhere)" just means that it goes from one place to another. You could also say, for example, "A storm is making its way down the coast" which would mean that the storm is traveling along the coast from its current location to the south.