zazanza: Ok, redownloaded the entire thing. Still, did not work. I've also checked my harddrive for issues, yet nothing. I don't know what else I can do at this point...
adamhm: Did you use the GOG.com Downloader or your browser to download the game? The GOG.com Downloader should verify the files it downloads so this doesn't happen, if you're still getting corrupt files despite that then something strange is happening... have you tried downloading from another PC? Also you might want to check the sizes/MD5 checksums of the files you downloaded with the info I posted earlier.
I've tried both the browser and the downloader, but both fail the integrity check. With the browser they fail instantly, while with the downloader, they scan for a few minutes (allowing me to skip the process if I so choose), reaches the end of the bar, before it fails.
I've not tried downloading from another PC, but this one has always worked for me before (both with GOG and other places).
The files I get look like this:
setup_alan_wake_1.0.0.12 (2 292 kB)
setup_alan_wake_1.0.0.12-1.bin (2 048 490 kB)
setup_alan_wake_1.0.0.12-2.bin (2 050 782 kB)
setup_alan_wake_1.0.0.12-3.bin (2 050 782 kB)
setup_alan_wake_1.0.0.12-4.bin (2 050 782 kB)
setup_alan_wake_1.0.0.12-5.bin (56 044 kB)