I wasn't assuming global nuclear war in that scenario. You can see a large increase in armed conflict around the globe due to nationalism sparking conflicts, without the US and Russia nuking each other, or the US and China nuking each other.
Russia goes into Belarus or Ukraine, maybe Kazakhstan. If you're a dictator like Putin and you can't expand your economy organically, you eventually try to do it through invasion.
China will go after Taiwan sooner than later. In another ten years they'll be close enough to parity with the US to likely do it and have the odds strongly in their favor of safely getting away with it.
The mess in the middle east will continue. There's still a high risk the US ends up at war with Iran, whether drawn in by Israel or otherwise. Saudi Arabia wants to become a nuclear nation. Both Saudi and Iran are practically guaranteed to reach for nuclear weapons in the coming decade or two. Saudi will want to get themselves positioned technologically in case Iran goes for that.
Japan will probably begin/continue gradually re-arming.
The major nuclear powers will go on a nuclear weapon upgrade spree, in competition with each other. That has already begun. China's moves there will be very interesting, given their (supposedly) relatively small arsenal.
We'll very likely see the US, China and Russia deploy weapons to space. That'll add to the tensions.