I don't get the author's point really.

I don’t feel like I’m climbing a mountain, I feel like I’m playing through a gauntlet of single screen platform levels.

Those platform levels almost exclusively take you to higher grounds, unless Madeline is stuck in some place for narrative reasons (e.g., the hotel, and even then she's trying to exit it through the roof). There are altitude markers. The map is literally a 3D rendering of the mountain with an obvious progression toward the summit.

Both figuratively and literally, you are climbing that mountain.