I picked up Empire Earth 2 from 
gog.com but was having some issues with multiple-monitors.  After a bit of googling I came across a solution from someone going by galatei at 
neoseeker.  Add the following lines to the config.cfg (or config_EE2X.cfg for EE2:TAS):
g_bFullscreen = 0 
g_allowWindowedMode = 1 
g_ConstrainCursor = 0 
s_windowXOffset = 10 
s_windowYOffset = 10 
s_adapterIndex = 0
Worked for me in single player mode.