There is pretty limited casual effect between the WW1 "storm troop" tactic and what has become mislabeled as Blitzkrieg. As it is a sort of made up name, nobody is even sure quite what defines blitzkrieg. In his book "The Blitzkrieg Legend" Col Dr Frieser spends all of chapter 1 evaluating about seven different definitions varying from the strategic (get the war over quickly before more powerful countries can bring their weight to bear) to tactical (combined arms). In the end he concludes that whatever definition you like, the effects were the result of German operational necessity.

That divergence dealt with, the German doctrine in use was "Bewegungskrieg". A much less catchy name, but it means maneuver warfare. As a concept, Bewegungskrieg goes back to Bismarck in the 1870s, it's "The German Way of War" as Citino put it. The German military had, by 1939, over a half century of relying on maneuver as their method of making war.

After WW1 a series of assessments was undertaken by the German General staff, under von Seeckt. The conclusion was that they had the right idea all the time, they just needed to get back to implementing it. Insofar as the "stormtrooper" tactics relied on maneuver instead of firepower, it merely sat in the long tradition of bewegungskrieg and local decisionmaking, even though it was arguably too low a level to truly count as such.

As a result, it is fair to say that what is now often considered "Blitzkrieg" would have been an independent development no matter what the Russians or stormtroopers were up to.