I get the distinct impression that the writer views the lack of handyman skills as being effeminate (at least intuitively, perhaps not intellectually). I would, therefore, add a fourth class of customer to his list: people who are socially perceptive.
I'm not sure what you're basing that on? While the author indicates that he meets a lot of men who view a lack of handyman skills as not masculine , I don't see any indication that "not masculine" = "effeminate".
On the topic of your post: I was (more or less) using effeminate to mean "not masculine", with maybe some connotative meaning thrown in. This seems to be standard usage based upon my extensive perusal of the copious amounts of information available at http://www.merriam-webster.com/dictionary/effeminate