I mean I guess you could argue some calculation kind of looks like a type of random walk (with intuited moves) based search. But that's kind of all AlphaGo does, and it does it so efficiently that's all it really needs to do.
I'm not a go player, but at least in chess, which is game theoretically very similar modulo branching factor, human thinking is much more of a mish mash of different search methods, different ways of picking moves, and strategic ideas(which I like to think of as sort of employing something more akin to A* or Dijkstra).
I.e there's a rough algorithm like this happening
1. Asses the opponent's last move, using some sort of abductive reasoning to figure out what the intent was and whether there's a concrete threat. If so, try to refute the threat(This can sometimes be a method of elimination search(best node search is a similar algorithm) if the candidate moves are few enough, or a more general one if not), find counterplay, find the lesser evil, or resign
2. If not, do you want to stop their plan or is it just a bad plan?
3. If you do, how?
4. If not, do you have any tactical ideas? search all the forcing moves in some intuitive order of plausibility and play the strongest one you find
5. If not, what is your plan? If you had a plan before, does it still make sense?
6. If not, find a new plan
7. Once you have a plan, how do you accomplish it? Break it into subgoals like "I want to get a knight to e5"
8. find the shortest route for a knight to get to e5(pathfinding while ignoring the opponent)
9. is there a tactical issue with that route?
10. rinse and repeat until you find the shortest route that works tactically.
I could probably elaborate this list for hours, getting longer and longer. But you probably get the idea at this point.
You are definitely right that computer players are missing some kind of narative-based reasoning for their own moves and for their oppoents' moves. In go it doesn't feel that extreme though. We're taught not to hold too hard to our plans anyway, and most good moves from the opponent will have more than one intention. So you can't get that far relying just on reading what their goal is.
How computers think isn't exactly how we do, for go, but it's close enough to rhyme pretty heavily imo.
I'm not a go player, but at least in chess, which is game theoretically very similar modulo branching factor, human thinking is much more of a mish mash of different search methods, different ways of picking moves, and strategic ideas(which I like to think of as sort of employing something more akin to A* or Dijkstra).
I.e there's a rough algorithm like this happening
1. Asses the opponent's last move, using some sort of abductive reasoning to figure out what the intent was and whether there's a concrete threat. If so, try to refute the threat(This can sometimes be a method of elimination search(best node search is a similar algorithm) if the candidate moves are few enough, or a more general one if not), find counterplay, find the lesser evil, or resign
2. If not, do you want to stop their plan or is it just a bad plan?
3. If you do, how?
4. If not, do you have any tactical ideas? search all the forcing moves in some intuitive order of plausibility and play the strongest one you find
5. If not, what is your plan? If you had a plan before, does it still make sense?
6. If not, find a new plan
7. Once you have a plan, how do you accomplish it? Break it into subgoals like "I want to get a knight to e5"
8. find the shortest route for a knight to get to e5(pathfinding while ignoring the opponent)
9. is there a tactical issue with that route?
10. rinse and repeat until you find the shortest route that works tactically.
I could probably elaborate this list for hours, getting longer and longer. But you probably get the idea at this point.