Wow, that is an old tape drive. According to an ebay listing I found, it has a 34 pin floppy interface (as you stated), so that even pre-dates the IDE tape drives. It appears to be a 420 MB capacity QIC drive.
I don't recall Backup Exec for Windows Servers ever supporting anything like that. The oldest HCL that I see is for Backup Exec 10d, which has some Conner drives, but not that series. I believe that the Backup Exec you have is Backup Exec Desktop, not even a server version. I don't know if tapes are compatible between the two versions. Were your tapes still readable recently? I hope they haven't been sitting for 15-20 years.
I see that you can still download the BE Desktop software. I hope that helps you.
http://www.symantec.com/docs/TECH9434
It looks like it could run on Windows 2000 as the newest OS.
http://eval.veritas.com/webfiles/docs/bedesktop_pro_45_ds.pdf