I had this issue where it was playing in a tiny window mode - and ALT ENTER would not full screen it.

So -

My good buddy Collector runs the following site -

http://www.sierrahelp.com/Games/GabrielKnight/GK3Help.html

Edit the path of the shortcut and go into "Properties" to specify width and height (your desired resolution).

So for example - I changed mine to -

"C:\Sierra\Gabriel Knight 3\GK3.exe" -width 1920 -height 1080