There is no definition of AH anywhere,

Meanwhile:

    var
      regs: Registers;
    begin
      with regs do

AH came from Registers.

Overall, I'd say the author fell in between the computer generations. After things started to look high-level, but where a lot of the interesting stuff was still very low-level.

One of the first things I learned to do in Commodore-64 basic was poke53280,0 to change screen background color. It was low level for everything, and there was no expectation of the address or the value "making sense" as such; it was just hardware control.