It should be Linux-x86_64 package. Make sure there are no special (non-ascii) characters in game's full path — desktop folder suits well. There may be some Paper2D errors but such can be easily ignored 'cause game doesn't use Paper2D at all =) I'll try running the game on x32 VM asap.
Edit: it turned out that the game engine I use (Unreal Engine 4) doesn't support 32-bit Linux OS at all. Unfortunately, it's not what I can change, so there will not be 32-bit binaries.
Btw I googled a bit and it turned out that new versions of Wine are capable of running UE4 games like Mass Effect 1-2-3 :/