Setting a game against the backdrop of natural disaster can add flavour and drama to an otherwise mundane scenario.
To take just one example, flooding.
An underground dungeon is inherently dangerous during flooding as the rooms fill with water, necessitating water breathing, even far inland, and giving normally sea-bourne races a chance to shine.
Flooding can also act as a natural timer, the longer you wait, the more the dungeon fills with water and the more creatures and monsters are forced to head towards the surface, while you’re trying to get down. Much of this can also apply to modern or sci-fi urban games, or post-apocalyptic games.
Flooding can also have deleterious long term effects on areas in a game, leading to plot points and stories related to te natural disaster.
Floods can wash away topsoil (though they can also refill groundwater reserves and aquifers) and crops.
Crops that survive a flood can be stricken by mould.
Animals can be washed away or drowned.
They can cause migrations and emergence of monsters and creatures.
They can make people homeless or destroy their communities.
They can taint drinking water and flood sewage into living areas.
They can spread disease.
They can wash away roads and bridges, making travel difficult.
They can turn solid land into muddy swamp, making even everyday movement harder.
They can wash away woodland, orchards of forests.
The aftermath of truly terrible natural disasters can cause people to turn to banditry in desperation, can leave communities cut off and leave them to self govern. They can lead people into cultish behaviour, milleniallism, human sacrifice, zealotry and other dangerous mindsets – even foment revolt if their ruler doesn’t help them.
There are always second and third order effects to anything, it’s just down to you to think of them.