Telling someone that it's possible to beat a Super Mario game without jumping is like telling someone it's possible to eat pancakes without syrup. Yes, some people attempt to do it, but it's like committing a cardinal sin. Well, believe it or not, someone actually did manage to beat Super Mario Odyssey on the Nintendo Switch without jumping.
Now the really interesting part about all of this is that even though you can perform certain actions that are clearly jumps in the game, there's an in-game counter that actually tallies up whether or not you're actually jumping. In this case, the video explains that when Mario uses Cappy to capture objects, entities or enemies, and when performing jumps while those objects/entities/enemies are captured, it doesn't actually count as a jump.
I know what you're thinking "How isn't it jumping if I can clearly see them jumping?" Well, it turns out that at the end of the game when you check the stats in Toadstool's castle, it will show how many jumps you performed throughout the game. Gamechamp3000 revealed that when performing jumps through those you've captured it doesn't actually count those jumps. The counter stays still.
However, it does count Mario's variety of jumps, including his standard jump, long jump, double jump, triple jump, backflip, side-flip, and ground pound.
So Gamechamp3000 set out to beat Super Mario Odyssey without raising the jump counter in the game and see if it was possible.
Well, after encountering a conundrum at the very start of the game, the video manages to move onward to explain that it's possible to use Cappy without jumping and without capturing anything. Mario can throw Cappy, dive off Cappy, throw Cappy, and then dive off Cappy again for both horizontal and vertical elevation.
It's actually quite a fascinating video, as he explains some neat tricks scattered throughout Super Mario Odyssey that speedrunners have already uncovered that allow players to get around certain blockades that might force them to jump. For instance, in the 2D segments you're forced to jump, and the only way to not jump is to avoid the 2D segments. Well, in the Cascade Kingdom you can actually capture the T-Rex and use a jump pad to bypass the 2D segment.
In some of the other stages where the 2D segments are required to progress the story, it's actually possible to acquire enough power moons to bypass those areas.
After the initial run he did run into a problem where he jumped 29 times, but it turns out it was because it talked to NPCs. He redid the Super Mario Odyssey no-jump run and this time figured out a loophole to talk to NPCs without initiating the jump. He also ran into a problem with a cinematic that forced Mario to jump, but he also found a loophole to use the second Joy-Con as player two to avoid having Mario jump, which resulted in him completing the entire game with zero jumps.