I can well understand your eagerness to get the latest GalCiv, and how that eagerness can lead to missing a few important requirements. The description of GalCiv III in the Steam Store lists the requirements for running GC3. These include Windows 7 (as you discovered), and certain other minimum and recommended systems requirements, such as a Dual-core processor (minimum) or an Intel Core I5 processor or equivalent (recommended), 4GB RAM (min) or 6GB RAM (rec), 512 MB DirectX 10.1 compatible Video card (min) or 1GB DirectX 10,1 compatible Video card (rec), and a minimum display resolution of 1280x800 (this last has caused some confusion because the game lets us play at 1280x768).
You may wish to check the entire system requirements list Steam has for GC3 and make all of the upgrades you need at the same time.
Also very important: We have discovered (as is typical with any new game in an external Alpha test cycle) that current GPU drivers are also required.
I hope this helps, and welcome.