Is it possible for a prior service Marine to reenlist with a 6 year old DUI on his record?

It just depends.
Needs of the Army (Do they need HIM)
Criminal history (moral) waivers are decided on a case by case basis and depend on individual factors. Depending upon the needs of the military, and the past criminal history moral waivers are either easy to obtain or impossible.

Either USAREC has said no DUIs allowed, or something is missing here. How many different recruiters has he contacted?

It all depends on needs of the military. Standards rise and fall depending on the current needs. A war time military generally has higher needs and lower acceptance standards than a peace time force with lower manpower needs. It has been possible in the past but it ultimately depends on current needs and current policies.

You already answered your own question: DUI. However, the recruiters should be a bit more professionals and close the loop with him. Unless, there’s more that you don’t know.

If its a DUI, he should seek legal advice and see how to degrade it to reckless driving, or something like that. It might help / might not help. I’m not a lawyer and I’m not giving legal advice!!!

I came out of recruiting in 2019. At the time if a person received a DUI during or after service there was no waiver authorized. Kind of like you should have known better. DUI before service could receive a waiver. Things change pretty frequently and I don't know what the current message is though.

The problem here isn’t the DUI in itself. The major issue is that he got it either in the service or since he separated. The Army looks at it as once a professional always a professional. There is a small chance he can get back into but as a current recruiter... it will be a tough sell and a long shot

Honestly? He’s got like a .05% chance.

If the recruiters stopped talking to him, it's because he's no longer a viable prospect. That alone is an answer to the question.

His ENTNAC may be pending after the bright lights and rubber hose to get him to spill his guts. May be more to the story. Recruiters don't approve enlistments, they process them, provided the applicant is mentally, morally, and physically qualified. Then MEPS and the Service become involved. Service policy is what matters most if he passes MEPS.