Re: Atemi and Aikido
Thought I would chime in, and say I'm pretty sure the first video is Aikido S.A. (Shoot Aikido (Shoot is sort of Japans MMA in some ways)).
Not 100% sure, but I've seen it referenced in context with A.S.A. and the dojos seem to be located at the same places.
My own, completely uneducated, view on it:
As long as you use the Aikido principles in your Atemi (and not just pure strength, for instance), I say it's still Aikido. Gozo Shioda talks quite a lot about the importance of Atemi in his semi-biographical books.