I assume that election works like Soviet elections, only with more of a Putinist flair?
(Blank votes count as for CPSU, only CPSU candidate can campaign, media controlled by CPSU, but token "opposition")
The way that the election process ITTL's Soviet Union works, is more or less as you said, basically a combination of OTL Soviet and modern Russian elections, as while there are other legal political parties that exist and operate, most of them are only allowed to exist so that the government in Irkutsk can present a somewhat believable facade that an actual Democratic process is occurring within the country, while a nominal multi-party democracy the CPSU controls every single aspect of the state; and only CPSU and independent candidates with ties to the CPSU have any legitimate chance at winning the elections.
Who or what is a Nikolai Yeltsin?
Boris Yeltsin's father in both TTL and OTL, and a politician ITTL.
That makes no sense but whatever
How does it not make sense?
I can't imagine what kind of hell the USSR is going through with Lavrenty "I Have A Soundproof Rape Room" Beria in charge.
Well at the point that my TL is currently at, Molotov is now the Soviet President, as Beria recently died via an assassin's bullet during a state visit to Washington, DC, but his presidency certainly did not help the Soviet Union any bit besides maybe his strongman tendencies working to help keep the fragile and crumbling country together, but the Soviet Union is nonetheless in complete and utter hell, and in the middle of a four way Civil War between the government, Republican partisans, Fascist partisans supported by China, and Central Asian separatists supported by Germany; through that is not entirely Beria's fault.