I think it is pretty clear that they are Talking about the Y chromosome, i.e. being born a different gender.

Yeah, they just had a bizarre way of saying it.

There's far less than one chromosome's worth of difference between me and a orangatan.

"Just a chromosome" is like saying "just an extra brain"

It can be pretty straightforwardly interpreted as a reference to the probability of being born into one gender or the other, which is roughly equivalent to a coin flip (not taking into account the higher chance of being born male, hermaphrodites, etc.)

It is roughly equivalent to zero. I as I am now couldn't be born with another chromosome.

Anyway, it could be interpreted as "If my parents had a girl instead of me, what it would be like to be she".

Isn't that what I wrote? I may not have expressed it clearly.

I have trouble grasping why this distinction matters.

My understanding was that when people make "If I were X" statements, they are referring to having a conscious experience different than what they are currently experiencing. They would still be themselves by virtue of being the conscious observer in that context.