A military ID may not mean all it should - years ago my old office charged some poor soldier stationed at Fort Lewis who cousin had stolen his identity, and among other things had his military ID (and looked close enough to get by). It was a miserable experience for the prosecutor, and a lot worse for the soldier. It was months of work to undo our part, and probably years of misery for him.
If he actually does not have a valid driver's license from anywhere, I would run, and run far and run fast. Very few (if any) functional adults with the discretionary money to buy a firearm will not have a DL. Anyone with LE experience will tell that not having a DL is usually a sign of some form of dysfunction in their life and probably not a person with whom one should associate, let alone do a gun sale.
That's part of the answer. The rest of the answer: if you are uncomfortable enough to ask this question here, you are picking up a hint that something is not right. If you have that feeling, there is likely a good reason, if not several, that you should not do this transaction. You have the absolute right to refuse to sell to anyone under those conditions, and I would say maybe an obligation. Run. Run far. Run fast.