Using Mac OSX external drive as network drive

To clarify.  
You took that screenshot when the MyPassport was connected directly to your computer via USB cable .. isn't this correct?
Both your computers are connected via ethernet cable to an Airport Extreme.

In effect the sharing of the MyPassport HD is controlled on the computer it is connected to .. it has nothing to do with the Airport Extreme

Sharing external usb drives on a Mac is done in the Sharing Preference Pane in the System Preferences
Ensure File Sharing is enabled
Use the + button to add the MyPassport HD or a subfolder on that drive as a new shared folder
Set the users which can read/write that shared folder

From the other computer [Baryon] ... when you connect to the computer [Topquark] with the MyPassport attached you'll see the shared folder as a volume you can connect to

"You took that screenshot when the MyPassport was connected directly to your computer via USB cable .. isn't this correct?"

No, Both computers and the My Passport drive [actually, a WD My Book Live] are connected to the Airport Extreme with CAT5 cable - no USB involved [the My Book Live has no USB connector]. Also, the connection is described as 'FireWire'  by OSX Disc Utility - why?

Starting System Preferences returns 'Preferences Error - There was an error in Sharing preferences'. Starting Preferences a second time works and file sharing and file/printer sharing is read/write for all.

Note that an HP P2055dn laserjet printer, also connected by CAT5 to the Airport Extreme,  is one of the shared devices and is available to all computers/users - including a WiFi connected Windows 8.1 laptop.

My goal, not yet achieved, is to have both OSX computers and connected devices to have r/w access to all resources.

Thanks for your help, now working to create mycloud.com. Upgraded My Book Live to latest firmware and hard at work setting up.