Not an IT guy, but I'm sure they can run a script to specifically pull out AS website bookings on QF and then provide a bonus on just those itineraries if they wanted to. They can identify issuing agents/locations as well through accounting processes. As you observed, this would require additional effort outside standard mileage tracking. It's simply easier to have folks register for the bonus and just encourage them to check out the new booking feature.

As others have noted, the T&Cs do not specify any limitations on booking channel, so I don't think there's a lot of risk to booking via one's preferred method.