It looks like something attacked the paint. The stickiness would indicate that too. I know that at least the modern hammertone type paints are lacquer based. I'm not sure if the old ones were. Lacquers tend to be a little more delicate than enamels IMO.
Hammertone paints are still available. The colors are limited though. You're not likely to get an exact match. IIRC you can make your own too. The internet can help you there.
It looks like only the bed of the machine is affected. I would remove it and only repaint that part. That or try to find one being parted out and buy the bed from it.
Rodney