Different explanation, and some of this ain't pretty. (Apologies if this is male-centric, but it's probably quite similar for women.)

Richer people (or, at least, socioeconomically comfortable people) establish masculinity and effectiveness by building successful families. If you're happy at work and your kids are doing great and you're intellectually engaged, one woman is enough for most men. That obscene sex drive of the 17-year-old (that, if it could be realized at that age, would be horrific) is long gone. At 30 with a decent socioeconomic life, you can be satisfied with one woman as long as she's basically good to you, because you're happy and don't need sexual variety.

For some men, this isn't an option. It might be a lack of long-term, decent employment. It might be a family situation that he can't extricate himself from. Or, he might be externally successful and have "the perfect life" from a distance but be ridiculously insecure. Most men who cheat are horribly insecure (which may explain their tendency to "cheat down"). I hate the stud/slut dichotomy because (a) it seems to equate insecurity with moral weakness (and while sexual immorality is revolting, promiscuity isn't necessarily immoral, even if unwise for most people) and (b) the truth is that most promiscuous men are just as insecure as promiscuous women, so there's no justification for the differential perception of male as victor and female as conquered.

If you want to go deeper into the theory behind this, humans actually have two sex drives, one geared toward r-selection and the other toward K-selection. Stereotypically, the r-drive is stronger in the young (15-25) and male; the K-drive starts to dominate at age 18-20 for women and 25-30 for men. The K-drive is the "work hard, build a nest, find one partner you really like, maybe start a family" sexual drive. But if it's frustrated due to socioeconomic insecurity, people are more willing to let themselves be distracted by the promiscuous r-drive. This can be OK if it's all consensual and no one's being cheated on... but if it's furtive and dishonest, it's awful.

This isn't about a difference in values between social classes. I don't think that there is one. The (small) upper class is its own beast and assessing it would take time from what I'm trying to say... but the truth about family values is that, from lower to upper-middle class, and in all racial and religious categories, and even between straights and gays these days... there's much more variation within categories than between them. The marriage gap isn't about a discrepancy in values or "morality" (if that even applies, and I'm not convinced that it should) but in behavior. We aren't more moral than the people in the ghettos. We just behave differently because we're under a different and mostly less severe set of stressors.

Plenty of people associate wealth with the opportunity toward promiscuity ("two chicks at the same time") but the empirical facts are that (a) promiscuity hardly requires money, social skills and tactics ("Game") being more important, and (b) most people who are socioeconomically comfortable have little interest in promiscuity after age 25.

Comfortable people (a better adjective than "rich", because some objectively rich people are financially reckless, uncomfortable, and miserable) are more likely to marry because, with a low level of stress, most people are influenced much more strongly by the K-selective sex drive after age 25 (if not earlier).