The hinges on my table (the part that 2Oldman shows) point up. The brackets on the wall (the red arrowed in your image) have the opening facing down.
Does your table have the support bar? As in your diagram, the support bar is attached to the wall and the table. When you raise the table, the support bar (and table leg) holds the table up with the hinges (2Oldman's image) in the brackets (the red arrowed in your diagram). Without the support bar, the table hinges would simply fall out of the brackets and the table would collapse to the floor.
I'm wondering if with yours, the support bar was removed. In that case, the hinges wouldn't work as normally installed. Instead, the hinges would have to face down and the bracket would be attached to the wall with the hinge opening at the top. Then the hinge would drop into the bracket and the bracket would support the table without needing a support bar. If that's the case, you should be able to find a simple L shelf hinge facing the opposite direction. That little curve in the hinge is for the support bar, so if you don't have one, you don't need the curve.
If you do have a support bar, then you should be able to simply flip the wall brackets and the hinge will now fit properly.