The Stream Magic plays files from the network, in this case, your PC. But the software needed to play Internet radio is internal to your network-connected (and Internet-connected) Stream Magic, so no PC is needed.
I assume you had Logitech Media Server software installed on your PC, so the PC had to be on for Internet radio. If you had LMS installed on your SB3 you probably could have streamed internet radio without your PC on as well, but few people ran it that way because the limited memory and processing power of the SB3 made running LMS directly on it quite slow.
Steve