Because it grants the federal government, not the states the ability to create laws of naturalization. The federal government then has all necessary powers to create laws as to how this naturalization procedure will be implemented. The federal government did this through the Immigration and Nationality Act, which in part clearly delineates the methods by which federal and state resources will be used. The statute in question acted in opposition to the aims of constitutional federal authority in this act, and thereby was nullified by the supremacy clause.
Nothing in this decision is saying that the state is disallowed from creating immigration policy by the Constitution, what it is saying that the federal government has immigration authority and the state is trying to screw with it. When state and federal laws conflict, the state loses.
If you're interested, here's the text of the 9th circuit's ruling:
http://www.ca9.uscourts.gov/datastore/opinions/2011/04/11/10-16645.pdf
Hopefully that clears up the confusion.