One should probably think either "of any other mall" or of "any mall", or "of all malls" + "in the area", but even so, I find it wrong yet: would it not sound logically that
'ABC MALL HAS THE BEST PROGRAM OF A MALL IN THE AREA?'
I am afraid your statement copies the structure of a different kind:
- This car IS (to be) the strongest (of all cars)(in this area).
- This car HAS (to have) the strongest engine (of all) (CAR ENGINES).
where
when one changed OF ALL CAR ENGINES with OF ANY CARS in statement no 2:
- "This car has the strongest engine of any car(s)", either with plural or singular, it does not look good to me (but then again, I am not a native in English).
Should it not be at least OF ANY CAR'S? (if that still sounds normal)
I understand TO BE THE BEST OF ANY OF YOUR KIND, but TO HAVE THE BEST (smth.) OF ANY OF YOUR KIND, that I DON'T.
When you use the superlative in a comparison - "the most" (just like "the most of all") - you mean "more than ANY OTHER" or "more than ALL THE OTHERS", and not "more than ANY OTHERS".
I think the problems occurred due to syntax, as "the most comprehensive loyalty reward program" (which already implies thinking "most ___ OF all programs") is followed by an "of" that (re)connects ABC Mall with the rest of the sentence.
Is just like `Peter Pan has the smallest hat of any man in this area', which makes me think that the hat does not even have to belong to him necessarily, he only somehow got it. But is that right to say?
I believe that 'OUT OF all malls in the area, ABC Mall has the best ___ " and "In this area, Peter Pan is the man with the smallest hat" work better, but I might be completely wrong.