They are being multiplied, as in drawing a rectangle with one side equal to each number. There's no 'first' and 'second'; the idea that one is a count and the other being copied shows a fundamental misconstruction.
I don't really support the pedantry that's going on in the grading, but I'm not sure I agree with you. To the observer looking at a non-moving rectangle, "length" and "width" are not interchangable. In the same way, there are indeed a "first" and "second" by simple definition of the way English/math notation work (in other words, "left" and "right".) The student was asked to use the "repeated addition strategy" and an "array" -- if the algorithm for doing those was taught using a specific order of the operands, the student is technically wrong to swap them. Whether or not it's fair or useful to deem them wrong when they are giving an equal but non-equivalent answer, or whether or not the algorithm should care about order when the underlying mathematical operation is commutative, are other issues.
Then we can only conclude, the syllabus is teaching nonsense. They are structuring things that don't need (and shouldn't be) structured; they are instilling fake rules in plastic young minds that will take enormous effort to unlearn later.
Math is important. Teaching some witchcraft-inspired rote math is destructive to real learning.
And rectangles exist regardless of how you view them. If I approach your desk and see the rectangle from the side, its the same rectangle. Even from a corner. Even in a mirror, its the same rectangle.
Reading the BS rationalizations in the linked-to artcle and I'm beginning maybe the problem with math education is learn-by-rote teachers who won't think for themselves.
Yes, the difference between length and width is only one of perception or orientation. I emphasized it because I felt like you went too far in the other direction, almost implying that which axis is which doesn't matter geometrically. A 5x3 rectangle drawn in 2D space with labeled axes is not the same as a 3x5 rectangle, even if they have equal perimeter and area. There might be some value in trying to make sure the student understands that.
The act of calculating the area surely does mean they are the same rectangle. Because they can be written down in more than one way is a weakness of the notation; the math is independent of that.