The chart is all technically true. Finland was united in a crown union with the Russian crown, when the tsar abdicated, the decision was made for the Finnish parliament to take up sovereignty in his abscence. Thus, in a sense, you could say that Finland maintained the claims of the Russian crown in that the same instrument of government was continued and responsible for the transition to a republican and independent Finnish government, while the Russians overthrew the old regime entirely and replaced it with the shiny new Soviet system.
No one takes it seriously though, it's really just a kind of historical joke, and as the chart alludes to, there are more claimants to the Roman Empire than residents of the city.