I wonder whether your problem is somehow with the "parallel port card." Most Apple/other laserprinters require almost nothing in the way of drivers .... Laserwriter extension, desktop printer ext, and other extensions handle practically anything, the Printer Description simply notifies the computer of the capabilities of that specific printer (page sizes, duplex etc.DPI settings etc.) and most laser printers will run ANYWAY if a 'generic' PPD is selected.
The second element is the line of communication between the 'host' and the printer (whether through LocalTalk/Appletalk etc). I know NOTHING parallel port cards or how they should be set up to communicate with the host … but I am fairly sure that getting hold of the printing software is EASY (you probably have it already installed) . Whether it is possible for this printer/ your G3 to connect via Ethernet, I don't know .... there used to be a way but getting hold of the bits NOW would probably be very difficult.
If you are using a standard install CD, does the CD 'know' about your parallel port card or how should this line of communication be set up?, my suspicion is that (given the age of the printer), parallel port was included in order to make the printer PC compatible rather than for Mac use.
Apologies if I'm talking nonsense (which I may be as I don't know anything about THIS printer … had many Laserwriters though) ... don't know anything about Parallel port cards and don't know which G3 (beige or later?). But, MAYBE you are asking the wrong questions, and should be asking HOW the laserwriter should be set up to talk to the host through the PP card.