1920x1080 would be 800x600 back in the day, something everyone used for a viable (not just usable) desktop in order to be confortable with daily tasks such as browing and using a word processor. Not top-end, but most games would look nice enough, such as Unreal, Deus Ex and Max Payne at 800x600, which looked great.
Ditto with today's 1920x1080 desktop resolution on my Intel NUC and games at 1280x720.
But I could run 1280x1024@60 if I wanted. And a lot games would run fine at 1024x768.