It says they didn't actually fight head to head but did so through passive means? Like politics and stuff. I'm just gonna make a war game between United and Soviet but that won't be historically accurate..can I still do it?

They fought wars through smaller nations like Vietnam and Korea. The US was trying to stop the spread of Communism, while the USSR was trying to spread it. 

There are a lot of wars and events you can do: Vietnam War, Korean War, Angola Civil War. I don't recommend a war directly between Usa and Ussr. It's inaccurate

Yes. It's really really inaccurate to have the US and Soviet Union fight head on. You can describe proxy wars like the ones stated above.  Honestly, I think they're as heated as any regular war is.