I didn't know Wine had this problem with GMS games, I'm sorry to hear that. I searched a bit online, it seems that Wine has an issue with the Graphics Device Interface API. The best I can do for now, is recommend you to try it with different Windows Emulators, like QEMU.
If I find out any information that might help you to run my game on your device, I'll let you know.
Also, when I have a working Linux build, I'll make sure to notify you ;)