It's a bloody business and they were a bloody regime, killing was high on their list of priorities as any student of Soviet history knows. Hesketh-Pritchard mentions how in the trenches he was called "the professional assassin" in a semi-humorous way - only semi-humorous because then, unlike the fetish made of all things sniping today, picking men off like ground hogs wasn't considered sporting, gentlemanly or even humane - many on the Allied side in fact regarded it as at best unsavoury and "unfair". One comes across such sentiments in memoirs and even regimental histories of WWI - and perhaps WWII for that matter.
The Bolsheviks made a point of rejecting all such "bourgeois" notions of morality, and so I believe they were instinctively drawn to such direct, deliberate methods of killing, just as they were no doubt attracted by the idea of killing enemy officers in particular who they would consider political as well as military enemies. IIRC this political/class aspect comes across clearly in the movie. Some may think that's a bit thin, but one needs to have a sense of the foundations of their ideology and how such people see the world. They were determined to be different, to reject all that had gone before, if possible.
As you mentioned the regime clearly realized the importance of marksmanship and instituted a very thorough nation-wide program to encourage it - and that despite the fact that marksmen can be quite dangerous to despotic regimes!

That also demosntrates how important they felt the matter was militarily, and how clearly they saw such questions.
The Reichswehr did field at least one new scope and mount system in the Weimar period, and whatever pretenses might have been necessary before the repudiation of the Versailles Treaty, I think we can be pretty sure they continued to train and maintain schools or cadres. How much was done in
Russia
at the training grounds there is debatable, since most such work could be done easily in
Germany
without attracting attention from any Allied inspectors. If large scale exercises or formation training was done in Russia, then one would expect snipers to have been part of that. For example IIRC the German Army had a policy of using snipers and MGs as both cover and protection for each other, so if MGs were part of training in Russia, then snipers probably were also.