Pure guesswork follows.
Assumptions:
- you get two brackets and two of those screw/hook things per cabinet
- the cabinet back panel is set forward by at least the depth of the lips on the brackets
- the cabinet carcass is at least as thick as the width of the bracket from lip to outer edge
Screw the brackets to the top rear corners of the cabinet carcass, so the lips face away from the wall, towards the back panel of the cabinet.
Drill and plug the wall, and screw in the hooks.
Hook the cabinet brackets over the hooks, so they go into the vertical slots.
This way the weight is borne on the bracket, transferred by the horizontal lips to the top of the cabinet, transferred by the cabinet fixings through the sides to the base and shelves of the cabinet. The vertical lips of the bracket are used only for position.
(Clear as mud I suspect. And as I say, pure guesswork, especially as I don't quite understand what you mean about the hooks not slotting straight in, and needing to be rotated on two axes. Maybe the back of an envelope will help ...)