Here is a clip of one of my favorite Aikido gurus doing atemi. He applies atemi many times without doing anything else, but you can still see the technique. Even though he does not do an irimi nage, and only does atemi, it is still there. In this way, the atemi is uniquely Aikido because the principle and essence of technique, such as irimi nage, is necessary to properly execute the atemi.
With blushing cheeks I must admit that I am not that fond of the solutions shown on that video. They are techniques done almost solely with atemi. Let's call it "ateminage" - uke falls because of the strike.
In my perception of it, Nishio sensei's way of using atemi was more in line with what I would call aikido atemi - they were entrances and distraction strikes, leading up to proper aikido techniques, which were not done in a striking manner.
Myself, I experiment a lot with trying to do aikido techniques so that atemi are not needed. Whether I succeed or not, I like the idea, so it's worth trying for some years. I find atemi often applied as an "easy way out" - forcing uke to yield or fall, without tori taking the proper trouble to learn the technique well enough to work by itself.
Not that I don't also enjoy a few good atemi between friends...