Ive had this issue since I purchased the game on steam on thursday and Ive looked everywhere online and not found a solution.
Ive tried everything that could be related and eveyrthing they suggested on their website, the only thing that helped was changing the settings on NVIDIA control panel, AA and super sampling seemed to help but only when the game is fully zoomed in the unit/buildings textures were fine, otherwise the white squares are still there 
Hope you find a solution...and post it here...
I have a support ticket on the stardock website and no reply for 4 days, by the looks of it Im going to have to return this game without even a chance of playing it 