Thanks for that overview. Regarding classifications, it is helpful to understand the proper terminology. I'm also interested in a slightly different question — how are determinations of biological sex made? What are the essential criteria for being male or female? Are these criteria in contention? The article, for all it's limitations, seemed to justify the argument that even a chromosomal test isn't really sufficient, and minor deviations of genetic sex traits might be more common than realized. Are any abnormalities, whether chromosomal, genotypic or phenotypic automatically grounds for the intersex designation or just major and obvious ones?
Biological sex determination is made at birth (officially by a doctor or other qualified medical professional) solely based on the infant's genitals and chromosomes. So you are assigned as either male or female; since those are the only two sexes legally recognized, and that is what goes on your birth certificate.
XX + vag = female
XY + twig & giggle berries = male
In the rare case of intersex; and this is where controversy comes into play, the doctor will make the call to assign one of those two sexes. Depending on the country and laws the doctor may also perform surgery on the infant; with or without parental consent/involvement to make the genitals match the sex that they assigned.
One big problem here is no one knows which way the person will develop when they hit puberty. Luck could be on the person's side, they develop into the sex they were "assigned" and all is fine and dandy. Or they may have been "assigned" as being female, had surgery to make the parts match that, then develop during puberty as a male or vice versa. There's also issues dealing with genital mutilation, right to reproduce, disclosure, potential social issues, etc. Currently the legality of all this and being able to list intersex on the birth certificate is starting to be challenged.
Quick aside: I, and really no one in the public knows the medical details of that Olympic boxer person so I'm not making any claims here; just throwing out a possible explanation. They could have been born intersex, assigned as female on the birth certificate, doctor made parts match without disclosure, then developed as a male during puberty.
Not taking the social and legality of the above into account and looking only from a scientific perspective; classification of intersex is solely based on genitals and chromosomes, just like male and female. It does not take into account any minor deviations or abnormalities. So anything that is not specifically male or female as defined above would be intersex.
Remember, that article from a scientific perspective is being disingenuous and using false logic. It's attempting to make the claim that all DSD's are a form of intersex and making social, not scientific implications. It's trying to include such things as a female with slightly higher than average testosterone levels (even temporarily) as intersex. It also wants to include mental disorders that fall under DSD's as intersex. Intersex is a form of DSD, but that does not mean all DSD's are intersex. So no, there is not a broad spectrum of intersex. There is a broad spectrum of DSD's with specific rare ones being intersex.
Let's take a look at this from a different angle using Vitiligo as a comparison. Vitiligo is an abnormality in which cells that produce melanin die and manifests as white skin patches on darker skinned people. A black person with Vitiligo would not be classified as interracial the same as a person with a random DSD would not be classified as intersex.