Now, I never called Chrichton sexist, though I won't disallow the possibility. I found Chrichton pointing out that men and women both struggle with similar issues, as you mention, to be some of the better bits of the piece ("shreds of truth and insight"). This was particularly good:
When I look at people, I see individual human beings struggling to find love and fulfillment, using the skills that they have, overcoming the drawbacks that they have. Each individual human being has some behavior that he or she can do easily, almost without thinking, and other behavior he or she can accomplish only with painful effort.
From this individual standpoint, gender doesn’t seem very important. It’s a detail, like where you were born. I can’t say “All men are this way” any more than I can say “All Chicagoans are this way.”
Generalizations won’t hold up.
However, even though Crichton may not have been attempting to be scientific, his citing of science without reference severely detracts from the credibility of his arguments:
To take a single example, every good study of domestic violence concludes that women engage in it as often as men.
We are biologically frail: more male infants die in the first year of life; we don’t live as long as women; and we fare less well living alone.
These days, men and women can live comfortably as singles, and 25% of the adult population now chooses to do so.
I know some of this to be true, of course, but the lack of citations makes the claims rhetorically untenable. For my money, statistics mean nothing without a source. I also have no clue what he means by "[men] fare less well living alone." Does this refer to income? Happiness? I can't know without a source.
Now, a big part of what I take issue with here:
There is no question that men feel under attack, and psychologically beaten down.
I was not around in the late 80s, but somehow I doubt that the anti-male narrative was worse then than it is now. And I don't know about you (and it may be because of my personal choices in media consumption), but I personally do not see this kind of narrative, ever. I am a remarkably average-looking man, and I have felt personally attacked for my maleness a grand total of...once. I of course cannot speak for anyone other than myself, but I think the vast majority of MRA-type rhetoric is engineered to create outrage from things that are rarely an actual issue.
This is not to say that men don't face issues on the basis of their maleness; they do. This is not to say that some systems in society are unfairly biased against men; some are. But, in the grand scheme of things, bias (personal and systemic) against men pales in comparison to what pretty much every other group of people face. While the small amount of injustices against men should be recognized and corrected, much, much more time and energy should be spent correcting the injustices against those facing more substantial oppression. Chrichton's bellyaching about the stereotyping of men comes off as silly because the stereotype carries so little weight into the real world in comparison to other stereotypes (that is, men rarely encounter difficulties because of their portrayal in stereotype).