Determine device architecture (ARM/ARM64/x86) with 'adb getprop'
I did some poking around in some custom ROMs for x86 devices, and along with the info provided by @Izzy I think I've figured it out.

Example ARM64 device

ro.product.cpu.abilist32  armeabi-v7a,armeabi
ro.product.cpu.abilist64  arm64-v8a


Example ARM device

ro.product.cpu.abilist32  armeabi-v7a,armeabi
ro.product.cpu.abilist64


Example x86 device

ro.product.cpu.abilist32  x86,armeabi-v7a,armeabi
ro.product.cpu.abilist64


So, to figure out what kind of device you have:

ro.product.cpu.abilist64 not empty = ARM64

ro.product.cpu.abilist32 contains x86 = x86

If none of these conditions match, you have an ARM device