gut the car to frame and unibody, weld on front of 4x4 frame and rear of 4x4 frame to car. Find motor, cheap lift and big tires. Looks to be a 3 or 4 link rear though, or could have used a Jeep frame to start with.
Yea you basically just use a truck chassis/suspension/drivetrain. This guy just did a great job integrating it to the miata chassis compared with the normal "bolt the miata on top of a truck chassis" way of doing things.
Its tough to say, I dont know offroad frames well enough. It could even be custom considering all the suspension work and fabrication it would have taken to pull it off anyway. At least it is shortened to the point where it would be unrecognisable I dont think the pics are good enough to really tell, especially with a bunch of miata guys looking at it. I think it is actually pretty cool, although it would have made it a bit lower with a bit smaller tires.