The underlying point about spectatoritis is interesting, but I don't see what it has to do with what it means to "become a man" or developing a "manly 'philosophy of leisure'". Surely plenty of people of both genders are suffering from spectatoritis, and not only in spectator sports (and even there, there are plenty of female fans as well).
Nash's book is not explicitly gendered in that way, though it was written in 1938 and so does have a more implicit built-in assumption that it's probably addressing men (and it does use "man" and "men", but in the now-old-fashioned sense that's sort of gendered but ambiguously so and might also mean "people in general", depending on context). But it's not really accusing its readers of being insufficiently masculine; it's accusing them of being too passive, which seems more to the point.