It's the Jerry Lewis run.
I never earned a nickel from another man's sweat!

probably on roids.
"Hipness is not a state of mind, it's a fact of life!" - Cannonball Adderley

It's not just you - that dude's running is mucho weird. I always assumed it was some bad-ass Special Forces way of running down a Pentagon hallway in a suit in the most efficient manner. Did you see the way those goons jumped onto the roof of that building? They knew to drop and roll so they wouldn't blow out their knees.
P.S. I know you asked this question almost four years ago. But it's still a good question whose answer must be reconsidered upon each viewing of
No Way Out
.

The one with the dark hair is a goddamn ape. His arms are way long. Freakin' knuckle-dragging chimp.
Look at me, I'm Chandler could I BE wearing any more clothes???

The one with the dark hair is a goddamn ape. His arms are way long. Freakin' knuckle-dragging chimp.
Look at me, I'm Chandler could I BE wearing any more clothes???

nope, absolutely nothing weird about his running, said steven seagal
"the day I tried to live, I learned that I was alive"

really stiff. he clearly skipped his morning calisthenics.
today's special: shrimp ceviche!

haha i just watched this and me and my mom were commenting on his strange run

Reminded me of the two silent goons in Diamonds are Forever

I think that robot-like quality of the agents, Tweedledee and Tweedledum,
was intentional, to show what a couple of mindless goons they were,
in Contrast to Costner's passion and innocence.
Well, we think it's innocence until the very end of the film.

It is weird running.

Nope, the guy runs really weird.