Gender is as much biological as it is ideological, with no real boundry. Gender is more a spectrum in my experience.
Then again, I may not be the best to talk with authority.
Gender, in the sense they're using the term, is more ideological and psychological; it is biological only in the technical sense that abstract thought is ultimately a function of the brain. It is also, as Objective pointed out, bogus; like all ideologies.
omnia vanitasPhysical sex on the other hand is purely biological and completely independent of both thought and of the brain (and, in fact, of any organs other than the gonads) and, at its most fundamental level, is extremely clear cut - divided alpng lines of gamete production, you can be one or the other or neither or both. Anything else - in order to be found in a human - would require the evolution of either novel
mating types or of motile eggs and/or true and viable
spermatia and/or of viable gametes of a size and shape clearly distinct from both sperm and eggs. Some other species, especially among funguses, are divided along different lines but still generally produce some subset of a fixed set of mating types and gamete shapes.
EDIT:
On a less fundamental level there's a much greater number of potential combinations of physiological and neurological secondary sex charaxteristics. But they are all, as the category implies, secondary and non-essential features of said sex.