How to repair damage to finished fibreboard
Looks like someone opened the door with an object in the way. It's going to be very difficult to replicate a factory-applied vinyl coating as a DIY project. I'd contact IKEA about a replacement, or look for coordinating replacement doors from a local cabinet clearance outlet.

Otherwise, I'd shave out the loose, cracked, and bulged material with a sharp utility knife, then apply high-quality wood filler (Plastic Wood bonds very well and dries hard). Mask before sanding to minimize the impact to the surrounding area.