Very natural look, to be honest I am quite impressed that it isn't a industry standard right now and also that I have never thought that it was missing in games. I'd only tweak one thing: for a most natural look all surfaces shouldn't be "touchable" at all times. We usually touch barriers (such as at 0:25), wall corners around which we walk, some vertical bars, moving objects (doors, office chairs), etc. With these restrictions it would look absolutely stunning in a video game. Remove this restriction with some conditions (character is drunk, walking at height, instable for some reason, etc.) and it would really be a piece of animation I would like to be modded into every single game I own.
Game Development
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Honestly, I thought the character touching plain walls was a great way to support walking across or sliding against walls, which is common in games but doesn't make physical sense. When the character puts out their hand it can indicate that the character keeps its distance from the wall.
You may not put out your hand when walking along walls, but when you're pushed into them, you may very well put out your hand.
Another way to interpret it is the character indicating the restriction of the player's control. While the character will follow the directional input generally, when there is a wall, they want to and have to evade that. Putting out the hand gives it a human touch of looking for safety too - which could even lead to players keeping a little bit of distance to a wall when walking alongside it.