Well it certainly isn't Booking.com
If you go to the booking.com
How We Work buried in the very small links at the bottom you will find
So booking.com is relying on being an Agent.
It now gets really murky. Note that they work with "Service Providers" as well as hotels. If you search for
WebBeds, you will find that this is a part of Webjet - and it is
So the hotel presumably has some sort of contract with WebBeds who in turn are listed on booking.com. WebBeds looks like it is also an intermediary. As they claim
It appears that they are also strictly an agent (as they would wish to be).
It is most likely the Hotel itself is the principal here.
The attachment you included mentioned Agoda which is another brand / subsidiary of booking.com
You have not mentioned whether the hotel is part of a chain or an independent. The issue may well be that the individual hotel doesn't see the whole picture, or is not privy to the commission or rate structure, but it is likely that someone in the hotel hierarchy is - and that information needs to make its way to those that are responsible for creating tax invoices as well as those that should be responsible for accounting for GST, as they don't appear to be aware that it appears that the hotel is not properly meeting its obligations to supply accurate tax invoices (and pay the right amount of GST). This impacts on the ability of customers to correctly fulfill their own GST obligations.