I think the problem here is that the graph isn't defined to be a Finite State Machine. You need to have the template parameter isfsm set to true to enable incoming edges from empty space and to allow double clicking to define nodes as accept states. Try defining the template parameter field for your question or question type to be
{"isfsm": true}
I see I haven't documented that adequately; my apologies. I have now updated the documentation.
It sounds like I might have changed the default value of isfsm from true to false as our local use of GraphUI moved from its original use only for state machines to more general contexts. Sorry again, but as I said earlier I wasn't other of other people using the GraphUI.
I hope to push version 3.7.6 to github within the next day or two; this will contain the updated documentation.