Yep, after all, Soviet Union was widely known in the West as Russia, and containing of Russia was old Western doctrine...
It was old British doctrine..... until 1907. The US weren't engaged in any anti-Russian alliances until 1919 (and that was ideologically caused), France threw Anti-Russian sentiments overboard in the 1890s. Germany/Prussia had an on/off-relationship with Russia after 1890 until now, beforehands, Prussia was Russia's firm ally throughout the 19th century. Unless Russia's politics don't fall to wildly expansionist right-wing politicians (Hitlerowski or Mussolinowitsch?), I do not see much need for conflict on a global scale (small scale action to consolidate the borders, esp. in Asia, might be possible and tolerated).
As long as this alternate Russia / Soviet Union is neither
a) Communist
nor
b) lets its soldiers march through Warsaw, Beijing, Stockholm, Bukarest, Bagdad or Istanbul
there is no automatic line leading to a Cold War, or even to a bipolar alliance-system in Europe (let alone the world).
Also, such a Russia would be a Great power, doubtlessly, but without the ideological implications of being the Communist superpower, it would hardly be a global power meddling in Cuba, Angola or other very remote places. They would safe that efforts...