You have completely misunderstood the different measurements and what they mean.

A standard rack is specced as 19" or 482 mm. This refers to the maximum width of a chassis that will fit into such a rack. That Silverstone chassis is a 19" width chassis. It will likely fit inside your rack no problem.

The measurement for the Silverstone rails is likely the minimum depth, not width. These rails are designed to attach to the vertical rails that are at the front and rear of a rack. To properly support a large bulky chassis like this one the sliding rails are attached to both the front and rear vertical rails in the rack.

All you need to ensure is your rack has at least 570 mm distance between the front and rear vertical rails to attach the Silverstone sliding rack rails for your chassis.