So... Factorio works. I have not the slightest bit of a clue where the problem disappeared to but it did anyways. Bought the full version just now, no problem with that either.
Thanks for trying to help anyways, FishSandwich.

Ugh, can't believe I overlooked that. Sadly, the issue remains. Experimental demo log file is about as helpful:

0.001 2015-04-13 23:23:50; Factorio 0.11.21 (Build 13994, win64)
0.001 Operating system: Windows 7 Service Pack 1
0.001 Read data path: C:/Users/AdminAS/Desktop/FactorioDemo_x64_0.11 ...

The title says it... the moment I launch Factorio.exe, it kinda... goes nuts. It starts opening and closing windows at insane speed for about half a minute before giving me the error "failed to create display". The log file is anything but helpful:

22:42:09 Info None: 2015:04:13; Factorio 0.10.12 ...