Vaguelity is a form of a many-valued time reference (e.g. soon, later, sometime, etc...) or probabilistic interpretations of treaties and contracts (e.g. loophole); it deals with reasoning that is approximate rather than fixed and exact.
Time Referenced
Child Riding in Car: When are we going to get there?
Parent Driving Car: Soon
Probabilistic Interpretation
The loophole he is trying to use is the vaguelity of the UN treaty claiming that only nations and govenments can't stake claim to the moon.