In their home market, Germany, Aldi (and Lidl) are not considered to be supermarkets.
The word "super" does seem a bit of hyperbole, I'd agree. But on the other hand, I'm an Aldi loyalist, having got tired of Tesco's excessive choice and high prices. Why do I need forty three varieties of beans? Or a store so large that stuff can go off between picking it up at the back, and getting to the till?