This one's pretty easy to explain actually.
The router is not seeing your USB devices directly, rather, the router is acting as a USB hub. The router has no idea what's being plugged into it, it just passes the connections along to your computer, and when you click on "Connect" it treats it like you're plugging the USB cord into your computer.
USB is unfortunately not a true driver-less connection, so it's nearly impossible for DLink to support every USB device out there, it's much easier for them to just create a hub situation so the computer thinks of the device as being local to itself, rather than a network share (which most USB devices can't do anyway).
While it certainly supports almost any USB device your computer has drivers for, SharePort is really more intended for printers, scanners, and other devices that typically only one person uses at a time. For a network storage solution, you really should consider a home server, or networked harddrive enclosure (which is actually a full blown computer in compact form anyway)