To set a widescreen resolution, you will need to manually define a custom resolution for the game to run at. This will require editing the games configuration files.
First of all, you need to make sure the configuration files exist - this is done by starting each game (and each expansion if you have any) at least once, and then exiting.
Inside your Quake 2 folder in the "baseq2" folder, edit the file
kmq2config.cfg and find the following lines:
set r_customheight "xxxx"
set r_customwidth "xxxx"
Change these two lines (the xxxx) to define the resolution you wish to run at. For example, if you want to use 1920x1080, set
r_customheight to "1080" and
r_customwidth to "1920". Be careful not to get these the wrong way around.
Then, find this line:
set r_mode "x"
This is the line that defines which built in resolution option is active. Set this to "-1" to enable your custom resolution.
If you find after making these changes that your field of view is weird or not how you'd like it, find the following lines to adjust your FOV:
set cl_widescreen_fov "x"
Set this to "0" to disable the FOV auto-adjust. Then, find this line:
set fov "x"
Change this to the FOV (in degrees) that you want, save your configuration file, and run the game. If you need assistance working out what field of view you should be using at your resolution, you can use the Field Of View Calculator on the Widescreen Gaming Forums to work it out for you.