I'm not sure if anyone has ever had an issue with some of the game screens being too big to it their computer's screen, but with a laptop this happens to me frequently. Yes, I have tried full screen.
My suggestion is to have some type of + - magnification button to zoom in and out for those who prefer bigger/smaller screens. Max Games has this feature on all of their games if you need an example.
i bet that one of the web browsers (chrome, firefox, safari, explorer) has this built in or as an extension for all web pages. try to find it. i know theres a lot of extensions for google chrome
i think that is your screen resaltion problem, the gamer should make it so it will fit to the screen but some times you need it biger to fit it all or so. and there is not much of a fix to that any thing is going to sistort the graphics and text a little.
to do a bigger screen thing for all the games would mean that ever last programer would have to make it in a smaller size!! and that is no fare to the programmer. idk it is a hard thing to fix sorry