He is legally married but it is not recognized for any Thai legal benefits thereof.
However, if he used the unregistered status in Thailand to marry someone else, he would still be open to legal penalty. That is why I say he is in a Legal Marriage. Even though he is unregistered, he would still need a divorce to be free of the marital obligations. As it is he is caught between. He gets none of the benefits and all of the liabilities of marriage.