Psychopaths are known for being very good at getting people to agree to things; they are described as very glib and superficially charming, which is why they excel at being con men. So it doesn't seem hard to explain how they manage to get married. What is peculiar, though, is how their spouses manage to stay married to them even after they find out the truth. There has to be some denial involved. If something like one partner belatedly coming out as homosexual is considered an obvious reason to invalidate a marriage, discovering that you married a psychopath can only be even more obvious.
I knew someone who I have since amateur-psych diagnosed as being psycopathic in part (not a real diagnosis). I met this person while they were going through a divorce. We worked together on a few things for a while - charm and glib is a great description. But I noticed a pattern of having no 'old friends', and also appalling treatment of women that went far beyond what someone might classify as 'rebound behaviour' as behaviour that seemed to take delight in degrading women and a need to find friends who delighted in the retelling. I moved to distance myself from this person in an unconfrontational way - I assumed they could easily turn violent if provoked. In the end I was proven correct as they assaulted their own father in a disagreement not long after. I don't know what is going on now, as mutual friends who I knew have also ceased contact.
The twist in all this story is that the divorce was initiated by him, not his wife. She was a nice and very normal person, and to her, staying married and having a father for their child was probably more important. The point is that many people will try and hold a marriage together for all sorts of reasons.
I imagine that the spouses of psychopaths would give those kinds of explanations for staying marriedf they were asked. But a psychopath would seem to be a poor choice for a parent or a spouse.
I know they are good at manipulating, but you would think manipulating someone into getting married is a bit far fetched. Conning their way to a sale, an investment, a favour, a promotion, sure... but that's because they are willing to circumvent the social norms that govern shallow relationships. Marriage is supposed to be a very deep relationship so I'm not sure that manipulation is the explanation.
A psychopath doesn't experience normal emotions, so they can't have a deep relationship, and they don't know what one is supposed to feel like. When I read Without Conscience, I was surprised to learn that psychopathy is a brain disorder that causes a well-defined set of impairments and is possible to diagnose fairly reliably.