I think the only right answer is 'it depends', as others have said.
If I use my legs to go to the nearest shop, that's about 10 mins there, 10 mins in the shop and 10 mins back - so half an hour, but definitely not 'a walk'.
When I used to drive, or if I go somewhere with friends, and I/we stop somewhere, there might be a 'wander around' if the stop is for anything less than an hour, but if we stop 'for a walk' it'd have to be longer; that has applied wherever I've lived in the world; anything less than an hour is not a walk, it's 'a look around', 'a bit of a wander' or 'a stroll'.
'Going for a walk' is to me a specific activity; walking to the library, the shop, the post office, the doctor is NOT 'going for a walk' even if it takes half an hour or more, but is rather using my legs as a means of transport to or from a local place.