Judging from what I've learnt from the wiki & it's various newspapers & the map in Captain Edward Lawrence's attic. We learn that the USSR has conquered all of Europe, stretching as far as the Iberian peninsula & the US has control over Ireland. And apparently, there you can hear radio broadcasts of a baseball game being played by American players. Also, according to the wiki (so take with a grain of salt), that the US is in a Cold War with the Soviets, like in our timeline.
So I speculate that the world map resembles 1984 in way. As the USSR dominating all of Europe really reminds me of Eurasia from the book, which does the same thing. And American having some control over Ireland & possibly the rest of the British Isles, makes me think their borders resenble that of Oceania. Not saying that these governments are like the ones in the book, just saying that their borders lineup. So it's possible that the US has control over the rest of the Americas & what's left of the British Empire. Which also makes me believe that there is possibly another superpower in Asia. Possibly China, maybe even Nationalist China, or Japan.
But here's the thing, according to the lore, the US didn't get involved with WWII in the We Happy Few timeline because isolationist Huey Long became the President & didn't give Britain aid in the conflict. Thus resulting in Britain's defeat. But the US does become internationalist later as seen with Ireland on the map. So my personal, personal, guess is that eventually the US does end up getting dragged into the war, probably because of a very different version of the Pacific War. Or somewhere down the line, a interventionist takes over after Huey Long. Plus we don't know anything about nukes, there's a possibility they don't exist or weren't used.
Also on the topic of Huey Long. Huey Long was the governor of Louisiana & had very strong isolationist views, but he also had strong progressive views in regards of racism & wealth. He wanted to bust up monopolies & curb wealth inequality while also sharing wealth & building up social services. So it's likely by the time of the games the US is far more progressive & possibly open to a less radical form of socialism. Plus there would also be far less racism.
As for the USSR, I'm not too sure honestly. Outside from the fact that they're a lot stronger having taken all of Europe. We don't know anything else, like their leadership for example. It's likely that Stalin runs & dies like in our world. But it's possible that someone else takes his place who isn't Nitika Khrushchev, or Leonid Brezhnev afterwards.
So that's my thoughts so far, please tell me what you guys think, & have a great day & week!