Chess were indeed extremely popular among ruling circles in Europe, and Russia wasn't an exception to this rule. While chess games themselves are quite ancient, as far as I'm aware, their modern age with some rule changes which made them alike chess we know today happened around 15th century. Still, chess were a well known subject in Russia, with some findings of the chess boards and figures dating them early Medieval times or dark ages. Despite active opposition from the church, this game captivated minds of both common people and Russian nobility alike.

Russian monarchy indeed has a long history with chess, with Ivan IV the Terrible being prominent chess player who, according to some sources, passed away during the game. New Romanov dynasty, established in 17th century, also considered chess to be a worthwhile pastime, largely because it was a part of intellectual training and part of military preparation: properly calculating strategies and estimating risks meant a lot in warfare, and chess could teach war leaders exactly that. Chess was the favourite game of Alexey Romanov as a part of his active military education acquired at young age.

In modern age, emperor Peter I actively promoted chess among his favourites and officers, including competitive matches to ensure best possible outcomes. So at least in 16-18 centuries Russian monarchs indeed considered this game to be a game of kings, suiting their position.

Sources:

Aexey Lobin's article, Military education of Alexey Romanov.

I. Linder, Chess in Russia.