The tapes in the picture are DDS and DDS2 standard, LOAF has a DDS3 drive, I've read back plenty of tapes in identical situations. And a DDS5 drive can still read/write DDS1/2.
Now as for the OS, in 1996 this would be either WindowsNT3.5, 4.0, and pre-linux Novell (3.x/4.x) . Arcserve can read back previous versions without any hassle, whereas backupexec only goes back a version or 2/3 depending on the build. I know linux can read raw and multiple formats, but never had the situation where I had to recover something from an unknown enviroment.
Now depending on how far you want to go, I'd ask around first among friends who have possibly disgarded old servers stored somewhere(a school is always a good bet).
Unfortunately, I(as in myself, maybe someone else does!) know of no way to let even a modern virtual serverplatform that can connect to a physical tape drive or even get the physical SCSI card to be adressed directly, so you are limited to using a physical machine with the proper OS that recognizes the installed SCSI adapter card for reading back the tapes. Maybe head back to that used computer store to try and find a early to mid-90's server that sports a SCSI card to connect your drive to?