You have a software issue, most likely. I have played many of the Gameloft titles on my Z1, such as:
- Blitz Brigade
- Dungeon Hunter 3/4
- World at Arms
- Heroes of Order and Chaos
... and maybe more, I might be forgetting some.
I haven't had any problems playing any of them, excluding the usual Gameloft bugs, which are really much worse on Android than on iOS (source: I work for Gameloft).
Furthermore, your Z1 should be capable to run ANY game, given it is designed for an android smartphone (not tablet-exclusive) and available on the Play Store. Literally any. It's one of the fastest phones on the market, which inherently makes it designed for gaming. You can also expand on that by adding emulators, which basically open the possibility for your device to handle games for the classic PlayStation, or other older consoles (or newer - PSP for example).
Thus, you should return your phone to the retailer and explain that there is some kind of (probably) software issue. Make sure to show them that the games were downloaded from the official Google Play Store, and that your Android OS was not compromised (you didn'r root it or flash it). If they say that these games really aren't compatible with your device - they are lying. In this case you should seek legal help.
