If we had a decadal resolution for DO events we would have more accurate picture for VGV's game, but you are right, it is a bit offtopic. Let me try to make amends.
If the point of the game is to raise awareness, then it is important that it has a good basis in reality, even after artistic freedoms are taken.
4C by 2100 will certainly have an apocalyptic feel but it will miss some very important tipping points that will happen on our way to 4C, ( way before 4C), that may provide a better setting for the game than 4C.
For example a BOE.
A BOE will have similar but worse effects than DO events in the short term. As the world transition from a block of ice on the Arctic ocean during summer to "warm" ocean summers there will be abrupt climate disruptions. However after sometime, perhaps decades, the climate should reach a new normal. That is the 4C world.
The look of the 4C world depends greatly on the human reaction to abrupt climate change. If we go to war with each other then you get a madmax world. Nuclear winter, followed by resumed warming after particles settle and radiation sticks for millenia.
If we decide to fight for survival and fight climate change instead of each other but we fail anyway, 4C won't be that much different than today except that first world countries will live like third world countries and there won't be third world countries.
SO much change will happen that no geopolitics can be predicted. You imagination will likely suffice.
Things that will become a permanent threat to humans that could serve as game mechanics.
Heat waves: heatwaves when there is no ice in the summer will be like nothing any human has ever seen. Temperatures will regularly climb in the 50's in the continental Northern hemisphere with 60's going from unthinkable to rare.
A well equipped traveling party caught in such heat wave will be slow down to a crawl for days or weeks. If they don't have water and refuge they are done in a matter of hours, minutes in the case of extremes. If they have plenty of water they can survive as long as they have refuge from the heat, probably somewhere underground or caves.
Monster snow storms:
This is a problem mostly for the northern most NH. A warm arctic ocean during summer means lots of water vapor. However warm the Arctic gets during summer, it will cool down to below freezing with the long Polar. This snow will bury entire cities after a BOE but, by 4C, remaining humans may adapt.
It won't be terribly cold, but the snow will be unpassable by current means.
Torrential rains:
We've all seen strong rain. But nothing like what is coming in a warmer world. Take the strongest rainfall you have seen and multiply it by 2 or 3. Rivers will from in flat land in a matter of days, making the terrain unpassable until the rains subside.