No, they don’t claim that - but they do see it as a continuous thing (Russian civilization and the genocidal threat they overcame). Also, it’s not just them who celebrate.
Russians are always conveniently forgetting that they were the other major aggressor of the European WW2 theater. Heck, the so-called "Great Patriotic War" starts in 1941, skipping over their alliance with Nazi Germany and invasions of neighboring states.