Intersting legal question

Yahoo news had a brief article about the Washington D.C. hand gun ban and the usual anti gun pro gun rights arguments were in abundance. But the fact that got me thinking was this paragraph.

"The city argued the Second Amendment's gun language applied only to the rights of states to maintain citizen militias and does not cover the ability of citizens to own handguns privately for other purposes."

If that is the case where does Washington D.C. fall They are not a state and the constitution does not include a provision for non State Districts that I could find. If I am wrong on this please point it out. So since D.C. is not a state two arguments could be made the first being that they have no state sponsored militia, or a Governor to create one, so no one could own guns.
Or that since there is no state government the second amendment is null and void in D.C. and that just opens a whole quagmire of legal nightmares about the 2nd amendment specifically and the application of constitutional law specifically.