The Empty Shop has no functional purpose. It doesn't sell anything and has no events attached to it. The reason it exists is that without it, the links to navigate the shopping centre would be misaligned.
Whenever a new store is added in an update, like the supermarket in 0.5.3, we check if there's an odd or even number of stores. If there's an odd number, the Empty Shop is added to pad out the links. See the image below:
View attachment 4448920
Thanks to the Empty Shop, the links to go forward and back in the shopping centre are on the same line, with the same link navigation numbers. It has no functional purpose, it's just for player convenience.