I noted that the chart only listed the states and didn't include DC and other territories.
Washington DC
Requirements
Proof of SSN
You don't neccesarily need a SSN if you can provide a letter stating you are ineligible for a SSN. You can get a SSN with the EAD, and so it follows you can get a license in DC now.
I'm still looking to see what the rules for Puerto Rico/ the Virgin islands/ etc etc are. I'll update this post when I find them.