I've implemented timers that had timeouts using unix timestamps, but only for multiplayer - when a player's attempt to connect to the server times out, etc.

Inside the game loop, we would keep the global tick counter that incremented on every tick, and timeouts would be based on that rather than on UTC.

The tick counter was updated only when the game logic was actually running. Our approach to pausing was to not run the functions that handled frame updates or physics updates, and to only run the rendering functions.

Generally we would never care about actual world time other than for some timeouts like for network (as the time passes for everyone), or for easter eggs like changing the tree models for Christmas or so.

I don't think anyone serious would implement event timers based on real time.