As the others said: Your ZIP drive wight fit into thze parallel port of the computer but that does not necessary mean that it can work there.
All I have heared is that you need the SCSI version. So no chance with a little adapter.
Long time ago I bought the "universal" variant of the Zip-Drive, e.g. with SCSI- and parallel-connection. (The same connector, some kind of auto detection probably. That works ok on the PC with the parallel-Port and on my A4000T on the SCSI-Port.
This Zip-Drive is however problematic for the SCSI-Bus. It turned out to be the reason for huge problems I had with CD-Burning!
(Now I have 2 SCSI-busses in the Amiga (The original one from the A4000T and the new one from the CyberstormPPC), so I use the original one more or less one for the Zip-drive only and the Harddisks and the CD writer are connected to the Cyberstorms SCSI bus.