bombmaniac-
First of all you’re oversimplifying. But personally I’ve read a few of the essays written by the great existentialists and I’m still not sure exactly how to define it. I don’t think it focuses on the question of are we real, as much as what am I (presupposing and not really focusing on the existence of ‘I’) and what is the meaning of life.
As for your question regarding simulation, I don’t know why you need to get so sophisticated. We all dream, and while dreaming, aren’t aware that what we are experiencing is reality. So whose to say that this is reality?