The Mac Classic, should have 1 ADB port and 2 Serial ports. One of the Serial ports is intended for printer connections. If the Style Writer II doesn't work on the printer port, you could try to operate it on the modem port, too. Just to mention, I guess it's not recommended to connect a modem or other bidirectional devices to the printer port, as it's an output only port. To put an output only device, like a printer, on the bidirectional modem port, should be no problem.
The Style Writer II seems to talk QuickDraw. I think you'll need to have some system extensions for QuickDraw.
If I remember right, in System 7.5.5 in the Menu should be a Control Panel to set up the printer connection, e.g. to modem port. If there's no hardware defect, and the Mini-DIN-8 connector cable isn't broken, why shouldn't it print?