Short Answer:
you can’t.
(well, you can, up to a point – see below) as – simplistically speaking – websites cannot access hardware and make it do things.
just imagine one were to be able to write script of some sort that accesses your/any printer from a webpage or something and forces it to print 100000000 pages automatically without you being able to do anything about it.

Long Answer:
Bearing the above in mind (again, somewhat simplified), it is – essentially – the printer that has to be able to control what does and what does not get printed automatically.

3 options spring to mind here.

a) Using a cloudprint service:
Your printer is registered to a cloudprint service and picks up and prints whatever is sent to that service
NOTE: Google Cloud Print will be disabled on December 31, 2020

For more info – and possible alternatives – please follow this topic/thread here (and of course feel free to contribute to it if you have some more ideas)

There is also the “WPPizza Autoprint” alternative available now.

b) Your printer is enabled to check a dedicated email account and prints whatever arrives at that account

c) Your printer can listen to some script/command.
GPRS printers – for example – usually have an API that one can use to let it do things
(probably to be used in conjunction with this)
as there is no generic/standard API that would work for all gprs printers it will be something you would have to script yourself

Additional Info
Clicking on the “Print Order” Icon in the “WPPizza -> Order history” will simply trigger the standard javascript “print()” command.
Whatever your particular device does from there is completely out of my hands and is nothing WPPizza (or any other software for that matter) has any control over – some devices might not even listen to the “print()” command at all.
So other than the above, I cannot tell you anything other than what is being said/suggested here or indeed how to make things work with your particular device/printer (you would need to consult your device’s manual)

If anyone knows of other solutions – or i am missing things – let me know and i’ll happily add/amend this here