Yes the keg has female threads.
I've never seen that before, interesting.
I forgot also to answer the Q - yes, the dip tube fits through the 'washer' so the washer sits around the head of the dip tube. So the washer surrounds the flare of the top of the dip tube.
One of my 10 gallon corny kegs (a very old one) has something similar, but I don't know where you can find a replacement.
It might be worth a call to these guys, as they carry some older keg parts (race track lids, etc.):
http://www.chicompany.net/Otherwise, maybe take it to Home Depot and see if they have something similar. Per the link I posted earlier, a rubber slip joint washer might work with a bit of sanding.