The skill for estimating others' emotional responses to various stimuli that compensates for the flaws of my own native circuitry responsible for the task. How would you call that?

The charitable way of reading that term is to treat "emulating" as a modifier of "empathy", as in empathy implemented through emulation of the other. I'm inclined to think this is also the intended meaning, if only because the non-charitable sense would be better expressed as "simulated empathy".