This report is based on the full version of the game (patched to version 1.1). I would not recommend playing the game without updating to v1.1 first as the initial release has tons of bugs and stability issues. Version 1.1 is a huge update (365 MB). Some have joked that this patch alone is big enough to be considered an expansion pack to the original (v1.0) release.
The video resolution can be changed in-game via the 'Game Options'->'Display Resolution' option. Unfortunately, it does not support/list the following three resolutions:
1920x1440
2048x1536
2560x1600
I tried to manually forced this by modifying this line under 'graphicSettings' section:
...
displayMode = "res_2560_1600"
...
in the following file:
'C:\Users\\Documents\Empire Earth III\profiles\\profile.xml'
But the values would revert back after you exit the game. If you make this file 'read-only,' the game will default to 1024x768. The maximum resolution that can be selected is 1920x1200.
This limitation seems to be hard coded into the game engine. I have as yet to find a way around it short of hacking the executeable or the developers releasing another patch (which is doubtful but one can hope). This is rather odd for a 2007 game not to support these resolutions.
A second look (prompted by cranky's comment) reveals it's missing two more resolutions that's available on my card:
960x600
1280x768
I tried forcing these in the xml file but it did not take.