Ah, you're right. I think jsgrahamus might be expecting result to be modified by this line:
(let (diagonals result row) (get-next-row board-size diagonals result)
But it just creates a new shadowing binding for result, which exists only for the lifetime of the let, and is lost once the let is finished. Think of let as pushing a new value for its variable(s) on a stack before running its body, then popping the new values off, leaving behind any preexisting values.
Yeah, makes sense. However, let always creates a new binding and never modifies existing bindings. That's why it makes you indent its body to the right. Compare:
(= x 3 y 4)
(+ x y)
(let (x y) '(3 4)
(+ x y))
The indentation is a hint that these are new x and y variables, compared to any earlier x and y variables.
Besides let there are indeed functions in Arc where you can pass lists or tables by reference (though not primitives like numbers or characters). However, it's usually a good idea to try to avoid these, again so you can practice a less imperative style of programming (http://arclanguage.org/item?id=19709). My usual approach is to first build a program with promiscuous copying everywhere, and then if it turns out to be too slow pick the 2% of cases that can speed it up a lot and make them destructive/call-by-reference, because the cost of doing so is that it makes the program harder to understand.