Here's the offer page: http://www.gog.com/en/news/get_empire_earth_gold_edition_free
Add this to cart and check out (you need a GOG.com account, but that's a small inconvenience): http://www.gog.com/en/gamecard/empire_earth_gold_edition
And have fun!
I remember wanting to get this game ever since I read about it in a magazine, and was pretty much the only thing I played for a whole year, beating up Barbarians, slicing up Englishmen, building one of every robot to see what happens and cheatcoding my way to wins vs AI because I was young and didn't understand any of micro/macro/hotkeys.
Thanks for GOG.com and Rockpapershotgun for directing me there!