Actually the only Amiga specific thing on the MiniMig appears to be the crystals for PAL display timing! You can flash whatever you like into the FPGA. Ok it'll only have 16bit wide access to 2MB of sram but that should be fine for emulating other 68k based 16bit-era consoles.
An Atari should be fairly easy, but Neo-Geo and Megadrive should also be possible because they both used 68000 cpus and long as room can be found in the fpga for their other custom processors then there's no reason for them not to work.
I started to have a look into what else would be required but my knowledge of Verilog/VHDL is totally insufficient for working out the *how* to do it at the moment.
Andy