I dont really see that it matters much, but after watching that VERY classy video clip - what a corker - I was intrigued enough to put sharevari into google, and according to the top hit
http://www.metrotimes.com/editorial/story.asp?id=2691 Sharevari was the first, although the article was for the Detroit Metrotimes, so possibly not the best source. The liner notes to my "Motor City Machine Music: An Exploration Of Cybotron" CD reckon that Alleys Of Your Mind was released just before, so who knows.
I dont really care, but in the process of being inconclusive, I've just learned a hell of a lot! And just to confuse things, it seems that the first tune Juan and Rick Davis did together, possibly even before they called themselves Cybotron (notes arent clear on this), was Cosmic Raindance, so while it wasnt the first record, it was maybe the first "techno" tune!
But as other people have pointed out, I think its pretty hard to pick one tune and say this one is responsible for all the others that followed. When it comes to techno, you'd probably have to go back to some guy beating two rocks together whilst looking at the stars or something...