From what I could tell, Nishio Sensei seemed to be explaining how to properly attack in Aikido practice, and not how to do Aikido atemi. I mean, I don't know how knowledge of how to do a proper shomen strike as he explained can be used in any way to facilitate technique, take uke's balance, etc. He does demonstrate atemi in an entering move for his shiho-nage, but he does little to explain how exactly to execute the atemi. Maybe I am misunderstanding, but when we speak of atemi in aikido, it is meant as what nage does in technique, correct?
I think Aikido atemi is unique to the martial art and isn't necessarily derived from any other art. The execution of atemi seems to come about when one adds "corners" to a round technique. It is not something like "do a kick here", or "do a punch here".