What would it even mean in practice for them to think about concrete "walking" instead of the abstract concept? Verbs are inherently abstract.
When I was with my dog in my parents' house and said "spacer" (walk in Polish) - he was happy and jumped around in anticipation, bringing the leash. He did the same in my grandparents house even though we weren't going to the same place - he just wanted to go on a walk doesn't matter the area. What's your explanation that does not involve abstracting the action from the concrete area and time?
Another example - my sister trained our other dog to bring her plush toys on command. She hidden them in house and said "szukaj" (search) and then rewarded the dog with a clicker and/or a treat when the dog brought her the toy. It takes several steps (first you hide the toy very close and then you hide it outside of view). Also you reward the dog with the clicker on intermediate successes like getting the toy without bringing it to the owner.
Anyway - one time my sister lost one glove when we were on a walk with that dog. She noticed only when we were returning from the fields. She gave the dog the other glove to sniff and said "szukaj". Ciri (our dog) went back a few hundred meters searching for the glove and found it and brought it back.
There are smarter and dumber dogs (Ciri was probably the smartest dogs we ever had) - but the ability to generalize and reason is obviously there. Like - I can't imagine an unbiased scientist having a dog for extended period of time and not seeing it.
Dogs also have theory of mind (I've seen Ciri bury a bone in one place, wait for our other dog - Jaskier - to go home, and rebury it elsewhere).
Dogs also know which things are forbidden, and know that the things that are forbidden - aren't forbidden when nobody's there to see them do it :)
We also had a pretty aggressive dog before that - Kuba - which used to pursue neighbors cat when it came to our backyard. The backyard was fenced, and when the cat could see our dog - he wouldn't come. So our dog pretended to be asleep or hidden and waited for the cat to come, then he pursued it up a tree and waited under the tree till we came to free the cat.
This requires reasoning. It shouldn't be surprising - these are social animals that hunt in packs, cooperate, play pack politics, and need to reason about others in their pack and about the prey. How would they survive as a species if they had to invent pack tactics from scratch every time they hunted? Obviously they can generalize.
I find most of these arguments against animals thinking either incredibly naive or biased. Like some people actually argue dogs are "meat automatons" with no capacity to think whatsoever. It's like fishers saying fish can't feel pain :/