Hi
I think that site (not sure if its even legit or not) "sells" a special version of the game commercialized by Trymedia company that offers a strange kind of demo: you can demo the full game (all scenarios) but play it for a very limited amount of time (20 minutes or so). After that time you have to buy it.
So probably you just downloaded the demo.
Its easy to see that a "buy or get for free" policy is not a very sound marketing strategy for a games shop
Yuo can get the regular demo, the good one (no time limit but only offers some scenarios and the tutorials) form here
http://www.ageod-forum.com/forumdisplay.php?f=115
And if you like it, buy the game on AGEOD shop,
http://shopus.ageod.com/game-description-American_Civil_War-659234.html
or on a retail shop... and you will get your own serial number.
The full game is not given for free anywhere.
Regards