Actually Burger King stole it from Primanti Brothers.
This is from the article you linked:
Never mind that Pittsburgh's been putting fries between bread for decades now, this is the future of fast food: Take some things you already have in house, gussy them up a little into a sandwich, then sit back and watch the Internet sizzle over the news. [Grub Street]
And this is from an AI search:
The idea of putting fries on a sandwich is attributed to Joe Primanti, who, during the Great Depression, began serving sandwiches to truck drivers in Pittsburgh. The concept reportedly originated when a trucker brought a load of potatoes, leading to the addition of fried potatoes to the sandwiches, creating the now-famous Primanti sandwich
Amen. Or pulled and placed on the side if served on the sandwich.