I quickly had an attempt on the devboard.
Minecraft is no longer delivered as a jar which made it a difficult start.
I tried copying it off of a windows machine but it meant I had to find all of the dependencies on my own. I believe Minecraft is using a 2.x version of LWJGL which wasn't compile for arm at the time. There are currently 3.x version of LWJGL which are compile for arm (both 32 and 64bit). Of course, version 3 isn't a drop in replacement for version 2 (at first glance).
I had a look at the Minecraft for pi option but it seems to depend on native code for the particular CPU.