Huh, shows what Wikipedia knows. Bah!
Regardless, Kyril probably got on so easy because he was one of the first and loudest to make the claim in the 20s, and the British royalty was in exile in Canada, and they'd have to get their own house in order before they could consider buying a new one.
EDIT: Though that DOES give me the idea of including an option for one of the Windsors to be granted the Russian throne. It'd come at the penalty of being subservient to Edward VII and Canada, as well as a massive dissent hit from Slavic purists, though.
English Wiki might be taking sides or not being clear on the subject, I'm not sure and I'm too lazy to read the articles. The whole thing is a mess, what we basically have is a bunch of separate family branches with different views on situation. Russian wiki is surprisingly good though.
There are Kirillovichi, the family of Tsar Vladimir. Thing is, Kyril had no real legitimate claim to announce in the first place. His mother's religion doesn't fit the imperial law. He is eligible *only* in case there are no other proper successors.
Which existed (Romanovs back in 1920ies-1930ies) when he crowned himself emperor and were also pretenders. Kirill's children down the line broke a couple more rules from what I know and become even less eligible for throne.
Kirill-Vladimir-Maria are the heads of the imperial family basically because they decided to be so.
Kirillovichi are also somehow popular, which helps them to keep the status.
And then there is a Romanov Family Association which includes all the other Romanovs. They never really accepted Kirillovichi. This means Nicholas is accepted not as a successor of a Tsar Vladimir (who was not legitimate, as far as association concerned), but as an entirely separate head of Imperial family.
Now, the kicker here is - Nicholas isn't eligible for the throne either. There weren't any eligible Romanovs for a very long time.
The academic consensus is, at least in Russia, if you want to find a legitimate heir, you will have to dig deeper into the archives than those two families. Both broke plenty of succession laws. Without following the imperial laws there are a lot of candidates, some of which include the British royalty (Charles, I think, not sure). Or Stalin's children (Not even joking, we have monarcho-Stalinists, I find those guys hilarious)
Now, in Kaiserreich timeline we have:
Kirill. In game he is considered legitimate claimant for the throne and can be invited by a decision. (which lowers dissent, from what I remember)
His claim is still not valid though.
Dmitri Pavlovich. Now, Dmitri actually was the first in a legitimate line for the throne. Historically he screwed himself out of it in 1926 by marrying the normal American girl.
Assuming he didn't do the same thing in KR timeline (possible, since he is still in Russia and highly respected), out of two guys he is the more valid claimant. For some reason he is overshadowed by Kirill in events and him becoming the emperor causes some dissent.
Those two should really switch places or something.
It seems like I like talking about imperial family more than writing my thesis