I think he was talking about pointer from the "idea" point of view, not the language feature.
References in high level languages are mostly hidden pointers. A good knowledge of how pointers work is really important to get a good understanding of how high level languages work (a lot of Java programmers don't well understand the distinction between value and reference types, for instance).
Likely, be at ease with recursion is also very important as many complex problems are recursive by nature, and so way easier to solve using functional techniques.
Yes. Pointers are always there in programming and you need to understand how they work, even if you are using a language where you don't have to declare them as such explicitly.
I feel like this article on generalization could be a biography of my life based solely on the introductory paragraph, but I don't have enough time to finish reading it to be certain.
"Sometimes I felt that knowing Pointer arithmetic and tricks are some sort of chess-thumping that old programmers tend to do. (My background is system programming so I know how pointer works)."
Or the best, easiest and clearest way to do things... Sure you can write confusing crap with pointers, but they are very useful.
C/C++ programmers tend to do premature optimization (habit) due to the culture and the problem domain (past experience): device driver, kernel code, game development.
How important Pointer is for say learning any high-level programming language that don't have pointers (pretty much everything outside C/C++/Objective-C)?
Sometimes I felt that knowing Pointer arithmetic and tricks are some sort of chess-thumping that old programmers tend to do. (My background is system programming so I know how pointer works).
It doesn't matter what you know or learn during the university. What matters is whether you continue to hone your skill or not and have a high bar of quality.