Due to size constraints the game must be broken up into two parts, and the .exe must even be renamed once you download it because DA renames it. The two parts are the .exe and a folder containing configuration files. The .exe must be renamed "Equestria Kart (Kart Demo)"
Extract the .exe to a folder somewhere on your computer. Rename it to "Equestria Kart (Kart Demo)" Then extract the data (its all in a folder inside of the archive) into the same folder.
In other words extract both the data and the executable to the same location. Once you do this click on the game and it should run after you rename it.
I know this sounds very repetive, but I can imagine it's very confusing.
Link to me testing the game in unity: