That looks like it could be a thermofoil finish. Sanding, priming and painting can be done. There is a company you can send the door to that will fix it.

Zinser and a high quality paint should do it. There are also special primers and paints that you can use to repair melamine and I have had pretty good results with that.

You will never get one piece to match the rest, so be prepared to paint all of the cabinets.