Confusion from “men” , “the men”, and “the woman” in a same sentence
I think the author meant to say, "A serious undertone". The word "undertow" doesn't fit very well in this context. "Undertows" are "hidden", they're "dangerous", but they're not usually described as "serious". "Undertones" on the other hand, are very often "serious" or "sinister". So I'm calling it either a typo or a less-than-stellar education.
The definite article is used with "women" because the writer is referring to a specific set of women.
No article is used in the first instance of "men" and I can think of several reasons for this: a) the women pay men in general, not just the ones at this club; b) the writer wanted a little more variety of expression ("men", "the men" vs. "the men", "the men"); c) the article simply got left out unintentionally.
The definite article is used in the second instance of "men" because it refers specifically to the men referenced previously, and not men in general (even if men in general is what the antecedent refers to).
An undertow is something that sucks one down into the depths. The dynamic described by the writer may mean that either or both parties are being pulled down in this manner, and it may also suggest that the viewer is being pulled down into it. There is an energy here, a force that must be reckoned with.
Regarding your question about correctness of «"the men" are strippers ... "the women" are clients who pay...», that is correct, although none of the words clients, customers, consumers would be quite right to describe the women, who are onlookers who have paid a cover charge to enter the club. (I don't know just what word should be used.)
Regarding your second question, about "pay men" vs "pay the men", either is correct, but I think it's stylistically better to leave out that the.
An undertow can be "a feeling that runs contrary to one's normal one" (sense 2). Presumably that's the sense the writer is using. There's no problem with undertow; there is an undertow. The apparent problem is Yet, as it suggests "to the contrary", even though the sentence starting with Yet seemingly continues the same sort of thought as the sentence just before. However, the paragraph structure actually does work: 1, "law of the father ... overthrown", 2, "club is a playground", 3, "Yet there’s a serious undertow because".