NB! "[Någon] gick in i väggen" usually means that someone is depressed/weary due to daily activities. It is mostly used to talk about people having overworked themselves.
Yeah, it's pretty silly that they are using an idiom as an example sentence. The idiom is definitely more common than the literal meaning of the expression. In UK English you would say He burnt himself out.
So does this mean "He walked into a wall" or "He burnt himself out", or both?
It's far more likely to mean the latter. If, however, somebody actually were to physically walk into a wall, this would be the correct choice of phrasing as well. My dog has a tendency to walk into lamp posts when he's not paying attention.
I'm honestly not really sure whether this sentence really belongs in the tree or not, and I've made a note since earlier take a closer look at it later, for the next iteration of the tree.
Before reading the comments I was assuming that it meant "to walk into", as in "enter", the wall, much like happens in books and movies when magic is involved and passing through a wall will lead to adventure.
In this case, in i works like "into", but English has made a single preposition out of the two constituents. Generally speaking, though, in is a direction and i is a place.