Shortbread pans mostly appear to be either cast aluminum or ceramic with decorative patterns. Chicago Metallic offers a cast aluminum one.
Directions to reduce the oven temperature by 25 F for a non-stick pan were, no doubt, in comparison to a similar sized light colored sheet aluminum pan.
Cast alum. and ceramic pans would have different heat transfer characteristics more like your non-stick pan than a thinner sheet aluminum pan.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan