Eh, I still have a teeny 800x600 laptop. I keep it because it's a good ultra-portable wi-fi device with epic (9hours plus) battery life. I use it like an e-reader tablet and to take notes in meetings. It has an (approximately half-size) keyboard I can touch-type on (if I'm careful) and it can run 32-bit versions of all my regular desktop software. I often play a game on it to pass the time while on public transit or wherever, or take it camping to write with, or whatever. It fits in my coat pocket.
And, even on machines with lots of pixels, they don't all arrange them the same way. A "portrait aspect" screen on my wife's main desktop machine is about twice as many pixels high as it is wide. She uses it to do page layout for magazine articles, and having the same aspect ratio as the printed page is a win for her.
So, yeah, if you want lots of people to be able to play it, you have to be able to handle different resolutions.