What martial arts does Reacher practice?

He recognises reisy, which is a rare martial art. So he is very likely an expert of martial arts.

People like that usually use mixed martial arts. He is skilled with knife so probably not unarmed martial arts, from the way he held his knife it did not look like Krav Maga either.

He likely learned martial arts in US army, so most likely he started with "The Modern Army Combatives Program", which is taught in US army.

Tom Cruise's Jack Reacher (and Christian Bale's batman) used Keysi Fighting Method (KFM), but I don't think he used that here.

He's been a fighter all his life, since he was a kid. Ans, as the book explains it, he was a military cop, so he had to be a better fighter than any kind of regular or special unit and had a lot of special training.

Steroi-Do