Shimano 600 pedals are quality pedals, but yes they are made for use with cycling shoes that use slotted cleats. Most "track" pedals are, too. That vertical plate at the back of the pedal slides into the slot in the cleat/shoe.
Using sneakers with these type pedals like like using a butter knife as a screwdriver. Yes, it will work. But, there are much better and more durable tools for the job.
(I like analogies)
This is also like buying a $200 super-ergonomic backpack then loosening the straps till it swings back and forth as it hangs down by your butt...then complaining about your back hurting.