It looked to me like the corner was bumped at some point, slightly damaging the mdf and causing the vinyl to loose the structure it was bonded to. Particle type wood composites are very susceptible to moisture absorbtion and swelling which will cause further delamination. In your climate I would look at using a thin forulation of superglue applied very carefully to the mdf to seal and consolidate it. After first letting the superglue cure in the mdf, I would try regluing the vinyl with superglue. I would try using masking tape applied over the vinyl area you are trying to adhere so that the tape acts as kind of a "handle" to pull and hold the veneer into place without gluing my fingers to the vinyl. The tape would also help keep the glue off the face of the vinyl. To remove the tape I would peel it off starting from an edge farthest away from the repair and peel the tape off by pulling it back so it is folded over flat against the surface it is being peeled from. By pulling parallel to the surface rather than perpendicular you will avoud pulling the the veneer away from the suface it is glued to.
