The article did none of this.
It refers to the scenes between action sequences where the games slows it's praise down and lets the story breath. Where characterization and the well crafted world take over the shooting and explosions. It mentions the Tibeten village of UC2 prior to the climax of the game and praises interactions such as kicking a soccer ball. Heck it even says UC2 paved the way for cames like Journey, Dear Esther and the sort.
Erm, yes it did.
The genre has since come to be labelled somewhat derisively as "walking simulators" - a video game with precious little interactivity and no game-over state.
Of course The Uncharted games do have a failure state and you spend most of their running time engaged in third-person combat. On that level, they're still fairly traditional action games. But Uncharted 2 and its successors only dedicate a little over half of their running time to such mechanics. So what do you do the rest of the time?
Not a lot, interactively. Sometimes you simply watch cutscenes and have zero input whatsoever. The rest of the time you're being funnelled through intentionally frictionless scripted puzzles or button-tapping your way through automated platforming sequences. Technically you're still "playing" the game, but your agency is left out of your hands.
Now go back and read my post again.
I think the article is making the mistake of correlating walking with climbing, or platforming or whatever else, which is slightly unfair. I'm also not even sure the automated reasoning is as valid for Uncharted 4 either, since a bulk of the time is spent using the ropeswing, mudslides and the rock pick, which actually do generally require not only an element of timing, but also player control in terms of movement and momentum. Hell in my play through I died far more from failed platforming attempts than I did deaths from gunfights, which I think highlights this point.
With respect to the climbing itself, I think with that, similar to say Assassin's Creed, the gameplay factor is more in discovery than it is actual timing, in other words, figuring out where you can or can't go, which climbing route to take to get to a certain point etc, almost akin to an advance form of exploration.
Add to that, Uncharted is an action adventure game, not just an action game, so if anything the game is more true to it's actual genre than many similar third person shooters of this nature are. UC4 in many ways is a pretty even split between the two, as the genre name suggests. Only the adventure side in this regard refers to exploring, climbing, swimming, swinging, discovering, solving etc.