Thank you for the information.
The HP Smart Tank Plus Wireless 559 All-in-One Printer is mentioned in About AirPrint - Apple Support as a printer supporting the driverless AirPrint technology, so separate drivers would not be needed. Drivers/software from the printer manufacturer may or may not add functionality.
Normally, AirPrint requires Mac OS X 10.7 Lion or higher.
I noticed that this HP printer appears to require OS X 10.11 El Capitan or higher. The reason could possibly be drivers or extra software from the printer manufacturer.
Have you tried to set the printer up as an AirPrint printer?
You could then test whether it would work with your computer (without a separate driver) when running OS X 10.10 Yosemite. You would have to use a network connection for AirPrint, not USB. Reset the printing system and re-add the printer (now as an AirPrint printer). You may also have to check whether the latest printer firmware version is installed.
Reset the Mac printing system to solve a problem - Apple Support
Add a printer on Mac - Apple Support