So you're going with the "Everything came from the caveman's need for fire" argument it sounds like. Unarguably true if you want to reduce that far.
I still don't think you can come up with a logical example of Genetics being a war tool (yet) though. Yes Medicine has benefited from war time progress in many ways. But Medicine is not Genetics. While Genetics may be part of medicine (squares are rectangles but rectangles are not squares). All of the things you mentioned (surgery, rehab, prosthesis, etc) were practical medical applications for the battlefield, while Genetics was not created for or applicable to such things (although it has seen more recent attempts to apply it in that fashion).
Also business machines can easily be tied to war. IBM + Nazi Germany.
Finally challenge need not come exclusively from war. For instance using my example of Genetics, the challenge of explaining how traits are passed (or any sufficiently broad challenge), and being the first one to come up with it (scooping people and stealing their work to do so: Rosalyn Franklin) can drive people as well.
I don't disagree that war pushes innovation in any way. To say such a thing would be naive and ignorant of history. But it is not the only game in town.
Edit: Clarification of sentence structure.