Assassin of the Tsar might be a parable, for which I give the following view: the event was one of the most important in the Russia's history. Killing the Tsar was profound in the people's mind since common people looked at him with reverence. Moreover, his family and entourage of 9 people also was killed. This tragic event might haunt the conscience (in an abstract sense) of the Russian people. Its justification raises moral questions and now, after history showed the effects of Russian revolution, we can ponder about it retrospectively.
It would have been easier if the Tsar was marked by avarice and carelessness for his own people, decadent and a simpleton, as probably some communist propaganda movies must had depicted. However, the director chose to show him in a different light: he is studious, tactful and intelligent. On the other hand, the local chief NKVD-ist Yurovsky does what he does out of duty for revolution. One asks in the movie "Is it that simple?"
The interpretation might be extended as the assassin representing the Bolsheviks and the Tsar, the aristocracy/high class that was to be eliminated. In this light, we explain the following: Yurovsky is a approached by the mother of a girl that disappeared and he knows nothing about it. Doctor Timofeyev (the embodiment of "typical Yurovsky") worryingly speaks that he is not guilty about it. The girl's interpretation then is the mass of innocent people that died and suffered as a consequence of Bolsheviks' revolution.
Assassin of the Tsar is a fantasy/absurdist movie that is presented in a serious mode - respecting the subject by avoiding the dry humor that often accompanies absurd movies. I would interpret the second doctor (Aleksandr Yegorovich) as the embodiment of the typical light-hearted/forgiving part of the history.