[flagged]
But assuming you are being genuine: your sex (faka gender) is encoded in your DNA on the 23rd chromosomal pair. If you have two X chromosomes (XX), you are a female human (woman). If you have one X and one Y (XY), you are male human (man). These chromosomes dictate your sexual development (organs/hormones/etc). There are some people (estimated at 1-2% of the human population) who are "intersex", in that they don't have an XX or XY pair, but some variation thereof (XXY, XYY, etc). However even these variations generally fall under one or the other umbrella of male or female. e.g. Klinefelter syndrome (XXY) is generally going to present as male (albeit frequently with poorly developed testicles and other complications). Genes are complicated so this is a bit of an oversimplification.
To make this more about sex itself (since humans are a sexually reproducing species and that is why we are having this conversation at all), there are effectively three options for all humans: you produce small gametes (sperm / male) or you produce large gametes (eggs / female), or you produce neither due to some complication and therefore cannot participate in procreation. This is dictated almost wholly by your DNA.
So, back to the article: they know the DNA in the deer tooth was from a woman because (presumably) the 23rd chromosome was an XX pair.
The result is someone who may appear to be female, have female genitals, but has testes where ovaries would be expected. It's often not discovered until puberty doesn't happen as expected, and they discover they can't have children.
Like all these conditions, this is on something of a spectrum depending on how total it is.
As you say, genes are complicated. So much more so than is often implied in reporting of discoveries of "a gene for X".
To my knowledge there is no XX person who can produce sperm and there is no XY person who can produce eggs. So while "XX is female" is over-simplified, "XX is not male" seems fairly clear.
In no other field this combination (self-educated, actually knowledgeable, and calling customer support) seems to exist, so that alone might be worth further study.