It was pseudo-3D, I remember reading an article about how they made the sprites, but can't find that... wikipedia has

Donkey Kong Country was one of the first games for a mainstream home video game console to use pre-rendered 3D graphics

and they used SGI workstations to create the models and animations before compressing/converting them to 2D sprites

Rare invested their NES profit in Silicon Graphics, Inc. (SGI) Challenge workstations with Alias rendering software to render 3D models. It was a significant risk, as each workstation cost £80,000.

(sharing bc I thought that's a crazy amount of money for 1992)

IMO, that's all a part of the Rare+Nintendo hype at the time. Killer Instinct was in the same campaign for these pre-rendered 3D graphics as the wave of the future. Don't forget, they had to go toe-to-toe with Sony's Playstationat that time, so bringing anything that looked like real 3D on a SNES was kind of a big deal.