So they're more like democratic socialists than full-blown commies?
It seems more like they are Commies, who happen to win elections.
What is the defining difference between democratic socialists and communists who win elections? I don't think that the CPRF would throw the results out if they got voted out.
But they probably won't get voted out anyway because:
a) the Russian presidential system overwhelmingly favors the incumbent. The closest a non-incumbent ever came to beating the incumbent was 1996, when there was a 13.5% (~10 million) vote difference in the second round of the election.
b) the institutional problems of 1990s Russia will be dealt with to a significant degree by the CPRF.
c) the general idea of the TL is "what if Russia was lead by the CPRF?" so removing the CPRF would be kinda counter to that. No guarantees that "our Sashka" won't wind up leading the union though.