The manufacturer
https://www.gmyle.com/products/usb-class-2-bluetooth-4-0-dongle
does not list at being compatible with a 2008 Mac Pro, only 2009 and later. They list:
Mac OS:
Mac OS X 10.10 and higher (with built-in drivers, additional Continuity Activation Tools might be needed for Handoff, Instant Hotspot, and New Airdrop features)
Mac OS X 10.8 / 10.9 (with built-in drivers)
Mac OS X 10.7 and lower (need additional manual configuration for advanced users)
Note: This Bluetooth 4.0 Dongle will work for following models ONLY:
MacBook Air Late 2010 and later, Mac mini Late 2009 and later, MacBook Late 2008 and Later, MacBook Pro 13" Mid 2009 and later, MacBook Pro 15" Late 2008 and Later, MacBook Pro 17" Early 2009 and later, Retina MacBook Pro Mid 2012 and later, Mac Pro Early 2009 and later, iMac with Broadcom Wi-Fi chip Late 2009 and later)
Thus I myself would not purchase it.