The Y chromosome doesn’t carry much of anything. It’s basically just a carrier for the SRY gene, and in most cases, it’s that gene that triggers the majority of the sexual differentiation that occurs in early development. The actual “code” for what develops and how it develops is there for male and female differentiation in all humans, and it’s hormones and other factors that control whether or not that genetic code is expressed.

And in this case, we’re talking about stem cells (ie, a cell that has the potential to develop in to any cell, but hasn’t yet done so), and then artificially triggering those stem cell to develop in to sperm cells. A trick that can be done because the genetic code for it to do so is already there if the conditions are right.

As an aside, this is also why hormone replacement for trans people lets them develop secondary sexual characteristics that they wouldn’t otherwise develop. The code was already there, it just takes the right trigger to get the code expressing (in this case, hormones)