I really should have shown a side view!
So there are two pieces of veneer to cut: one larger rectangle with the Chicago screw hole (no inner rectangle cut), and one of the inner rectangle.
Assembly is as follows: Peel off all masking from all pieces. Place the larger veneer down, sticky side up, and place the piece of plywood that has the Chicago screw hole, the engraved magnet pockets, and the inner rectangle cut out, down onto the sticky veneer with the Chicago screw holes lined up. Now stick the smaller rectangle of veneer (engraved or not; you could also use thin leather here, looks nice) sticky side down onto the sticky veneer showing through the small rectangle cutout. This is your bottom half of the gift card holder. The top half is just attached with the Chicago screw. Glue magnets in (don’t forget to orient them properly so they don’t repel each other!) and you’re done.
Let me know if that’s not clear.