When we say WW3, what we really mean is nuclear war. All participants exchange their nukes and Russia and the West obliterate each other. The meek inherit the Earth, or what's left of it.
The thing to fear in the rest of the world is the utter destruction of trade, the ruin of the internet and radioactive clouds floating around poisoning people in far away lands. Civilization crashes and terrible famines wrack the world.
What's up for debate is how bad the ecological damage will be and whether or not there will be a nuclear winter. Some think the sun will be dimmed for years from all the radioactive dirt that gets thrown up into the sky. This may plunge the world into a nuclear winter that ruins and starves the rest of the world.
Or maybe not. Maybe it all falls back relatively quickly and the rest of the world can survive it, suffering only the famines and poverty created by losing most of Asia and North America. And probably Australia and New Zealand. If I were Putin I'd make sure to target New Zealand to get the Western billionaires hiding in their luxury bunkers just before everything in Russia was vaporized.
Nobody knows because it's never happened before. We'll just have to try it and find out!