the person here being quoted doesn't seem very clear about biology, for a biologist.
the SRY gene does not 'pop off' the Y chromosome. Rather what happens is that there is that the X chromosome is long and contains lots of genes, and the Y chromosome is.much shorter and contains fewer genes.
Now if you are a woman you obviously have two X chromosomes, and when eggs are formed then genetic material from the two X chromosomes can be split and rejoined essentially anywhere, as X is obviously the same as X .
Whereas men when they create sperm they have an X chromosome and a Y chromosome so the process of meiosis is not quite so easy as there's only a small area that's common between X and Y, and it just so happens that the SRY gene is located adjacent to that area, so it's quite possible, if rare, for SRY to end up on a X sperm, and also for a Y sperm to end up without SRY, since the splitting and rejoining of chromosomes is not a completely exact process.
Also it's not true that SRY is 'the' gene. Sex reversal can occur due to SOX9 or Dessert Hedgehog gene mutations.
And there really isn't such a thing as a 'hormonal male', that's nonsense. You do have 'normal male hormone levels' and normal female ones, but that's not a class of biological sex. A person with a male genotype who produces hormones below the normal male range, may have a female phenotype, but equally they might not. An old man with very low testosterone is in no sense a 'hormonal female', unless you are a fucking idiot.
And to whatever extent normal male or normal female development can go wrong, none of this defines a third sex. XX, SRY+ with a penis will be infertile.