How do we tackle the vision of the Edward Albee in "The Zoo Story"? To what extent did Edward Albee succeed in transferring his vision to the...

Well, if we were going to assume that each playwright has a specific, unified vision, we could not find it in a single work. Instead, we'd look at the entire body of work, published and unpublished, and would look at unifying themes and techniques.
That said, there may be reasons why the play was first produced in Germany. The vision it gives of America is an outsider's view, and not a happy one or unified one. Through the choice to have extended talk with very little action, then an explosive conclusion, we see disintegration of word and deed, and even alienation. In the specific characters chosen, and the reasons they both talk and clash, we see a hollow life. If we have to conclude what Albee's vision is from this, then, we see an unhappy one, and one that is going to be intentionally somewhat disturbing to audiences.