The primary thing when you take a sword in your hands is your intention to cut the enemy, whatever the means. Whenever you parry, hit, spring, strike or touch the enemy's cutting sword, you must cut the enemy in the same movement. It is essential to attain this. If you think only of hitting, springing, striking or touching the enemy, you will not be able actually to cut him.
Every single action Wick does during a fight is the one most likely to kill the most dangerous opponent in his immediate environment. He doesn't hold people down unless it's the only way to take a kill shot either at them or at somebody else, he doesn't shoot people in non-fatal spots unless it's the only way to take a kill shot either at them or at somebody else, and he never not shoots if there's an opponent alive within shooting range. They have to throw ludicrous amounts of people at him, or equally skilled ones, because otherwise things get solved awfully fast. And rightfully so: he's not fighting you, he's killing you as quickly as possible.
That's pretty much Mushashi's idea, mutatis mutandis.
By the way, I had a notion that he was the equivalent of a gun-totting Jedi, but that's wrong. Equilibrium's gun kata is Jedi gun fighting: quick movements, tactically slow, very showy. Knights, yes, pilots, sure, and I suppose they'd be good in an Special Forces role (but not against other Force sensitives, and leaving behind those damn lightsabers, unless you don't care about deniability). Not that they are ever used like that; for some damn reason the Republic deployed them in *command* roles, which is so medieval it hurts to think about. Nothing, ever, at any point in any of the movies, gives us the slightest reason to imagine Jedi have good strategic skills.
Or political abilities. Or an understanding of logistics. Or a workable intelligence system. Or are good at managing people. Or can use their precognitive and telepathic abilities worth a tactical damn beyond having good reflexes and (a couple of times) long-range communication.
Bloody plodding, obsolete religious military order of mystical metahumans. I think the Empire and the First Order are evil, and I don't approve of Order 66, but, really, let Luke or Ben be the damn last Jedi, and good riddance to the self-important wankers.
(I don't know why I went pseudo-British there. There's something about annoyed, layered insults against upper classes that just feels better that way.)