You write very well. It's as if your story s the beginning of a book. There are a few minor corrections though (mostly on the technical side).
It had been a long time since I walked those roads...
There's a rue of three when it comes to using an ellipsis. It's also required, for some reason established by the MLA, to put a space before each dot, so it should be "roads . . ." That also applies to:
And we both walked on....
but the heavy flux ofautomated vehicles and pedestrians
I think that the sentence isn't parallel because the first item consists of an adjective and a noun while the second item consists of just a noun (unless the pedestrians are automated which I think is possible since the setting is 2062) , so I think it should, maybe, look something like this "automated vehicles and busy pedestrians . . ." That also goes for:
brought afeeling of nostalgia and reminded me of some very pleasant memories
You could try "The building brought a feeling of nostalgia and reminiscence." Just a suggestion.
that are transitory and go by without making a difference to us
You could also try "There are some things in life that are transitory and ephemeral . . ."
Just like stumbling, falling and injuries
Here, I'm not sure if this makes it parallel, but you could try "stumbling, falling and injuring myself . . ."
It is irrelevant for what purpose the building is used now.
I think you should rephrase this sentence 'cause it sounds a little awkward to me. (It could just be me though. It's best to get a second opinion)
You also forgot to put commas before some of the coordinating conjunctions that connect two independent clauses.
I bought him a pack of M'n'M Mooncandies and we continued to walk.
Emotion is the thing that separates dance from movement and this was where I learnt to communicate in a way that transcends mere words.
Lastly, correct me if I'm wrong here, but I think you're missing the commas that come before the conjunction that connects three or more items (Oxford/serial comma)
Ex.
it taught me to be disciplined, to be persevering, to believe in myself and more importantly to love something passionately.
There should be a comma before "and" here.
Sorry if it seems like I'm nitpicking. I hope these are valid, and I hope these help. :D I really liked the story though. You connected the plot to your life very well.