An air carrier pilot reported seeing a single engine aircraft takeoff on a taxiway at RNO.

Narrative

After pushback and engine starts at RNO; we received taxi clearance: 'Taxi to Runway 16R via Taxiway H and Taxiway B.' As I taxied forward out of the alley; I noticed a small general aviation aircraft taxiing at a rapid rate on Taxiway B. The aircraft was moving very fast in the opposite direction to the way I was cleared. At the time; the First Officer was heads down with final weight calculations and reviewing windshear precautions for takeoff. A Standards Captain was in the First Observer's seat conducting a line check on me. As I stopped the aircraft short of Taxiway B; I incredulously saw the small aircraft rotate and takeoff just prior to the H-B Intersection. Had we been on the taxiway as cleared; there would have been a collision. I reported the incident immediately to the Ground Controller. I followed up with a phone call to the Tower Supervisor after arrival. His comments were that because of the windy conditions at RNO that day; the Tower Controller could not see that part of Taxiway B since my aircraft on Taxiway H was blocking that view. The ATC Controller filed a deviation for the small aircraft pilot; and was very apologetic to me.