Hm, I'm getting this same issue with Anomaly: Warzone Earth - Mobile Campaign. It plays the intro video's music in the background, but when I click on the app icon in my dock to focus on the window, it just shows a white screen. I've also tried running the actual application inside the GOG launcher, but it only produces the same result. I checked my Steam version of Anomaly Korea which seems okay, but my Steam copy of Anomaly Warzone Earth is broken along with other people saying
the same about Yosemite and these two games. I'm gonna contact GOG support about this issue.
Oh yeah, and for reference my system specs are a mid-2012 MBP running Yosemite 10.10.1, with 16GB of RAM and an Intel HD 4000.
EDIT: Messed up my link earlier. Sorry, not used to GOG's forum system!
Double EDIT: Never mind, apparently I can't upload my system profile to GOG because its too large (3.6MB).