While it technically works, having to choose between fucking up my resolution or playing with an enormous black border isn't what I'd call actually working. How can there not be some way to run it in a window?
I haven't tried King of Dragon Pass yet myself, but usually you can fix resolution problems like this under your graphics card settings. Look for something related to "scaling options" and make sure that scaling is enabled. I personally like to use the option "preserve aspect ratio" which will use black bars on the sides rather than trying to "stretch" 4:3 games into a widescreen view, distorting the image.
Unfortunately, many old games were coded with 4:3 aspect ratios only, so it's not possible to extend them into "true" widescreen without stretching them. So black bars on the sides may be unavoidable, but you should be able to get the game to fill the full vertical space on your screen without any trouble.
EDIT: Just saw elsewhere on this forum that the graphics card scaling may not fix the issue. Try the suggestion in this thread insead: http://www.gog.com/forum/king_of_dragon_pass/resolution_issues
Unfortunately that guy is just saying he rathers have his resolution set to 640x480 which is what I was referring to as "fucked up" in my first post. The problem is if it's set to that you can't alt tab out and have your desktop at the normal resolution. I may be in the minority but I use alt tab a lot so while the game looks better when it's taking up most of your screen it also makes my computer unusable until I quit.