All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The ideology of the Dorzi people is based mostly on disbelief doctrines, like those issued by the Permanent Committee of Fatwa in Saudi Arabia and which can be found in the link mentioned in the question; they also have other wrong beliefs.
Therefore, if this man believes in these ideologies, then his marriage to this Muslim woman is invalid; hence she should separate with him and not allow him to have sexual intercourse with her.
It should be noted that a Muslim woman should not accept to marry a man until she asks about his religion and moral conduct the trustworthy people who know him. For the conditions of a valid marriage contract please refer to Fatwa 83629.
Allaah Knows best.