Keep in mind they're not using MAME. MAME does things the "traditional" way and aims for no hacks and 100% accuracy, hence why it needs very beefy specs. What Code Mystics are using is a custom emulator that uses High-Level Emulation, which uses lots of hacks and essentially "cheats" to translate the machine code to native code in a very fast way.
Code Mystics have been commenting on reddit alot and one tidbit they explained is that instead of properly emulating the actual "Midway DCS" sound hardware used in KI and others, they ran an emulator through the sound data offline, allowing them to essentially render all the sounds and music "offline" in wav format. So what their emulator does, is when it detects that KI wants any specific audio file, instead of emulating the DCS system (which is CPU intensive), it just fetches the corresponding wav file and plays that. This saves IMMENSE amount of processing power. Playing a wav file is basically free. This is just ONE hack, and they have to be using many, many of them in conjunction to get fast speeds.
If you remember, back in the day there was the
U64 Emu emulator that could run KI on a 400mhz Pentium, and it used High-Level Emulation. This is the same deal, but more custom and professionally polished (U64 Emu had
lots of glitches and inaccuracies) This is how they can get that game running on such weak hardware.
Arcade1up have gone on record to say that KI runs on the same hardware as their previous Midway games. Code Mystics (who built the emulation) said their KI code is even less CPU-intensive than their NBA JAM one.