Other cities might refer to them as tennis shoes, or sneakers.
Andrew: “Hey, joe. Steve's party is tonight, and then we're going out dancing later.”
Juan: “I dunno, man. I'll go to the party, but I don't really have any clothes to wear dancing.”
Andrew: “Don't worry about it. It's so casual you can wear your gym shoes to the place. It's like this old abandoned warehouse where they play house music.”
Juan: “Alright. Lookin' forward to the brewskies and dancin' tonight!”
“Gym shoes” is from way back in the wayback machine, originating between the mid-1920s and early 1930s. Whereas most of the country adopted “sneakers” or “tennis shoes”, Chicago stuck with “gym shoes.”
This young lady is tweakin' and enjoying the smell of her gym shoes: