Well the damage has spread to areas besides the full colour area. As the pic shows the damage is quite widespread. The scary part is the differing colours with the words and numbers in the middle.

Hmmm I wonder if there is a way to "glue" the paint back down.
You could try PVA wood glue, working it under the cracks with maybe a cotton bud, then cover with glad wrap and clamp flat with some timber, the glad wrap will stop the timber sticking to the playfield, and when dry it will peel straight off.
Do small areas at a time otherwise the glue will take a long time to dry.
Any excess glue can be gently wiped off the surface with a damp sponge or rag afterwards.

Might be worth a shot, you could save a bit of work and the art.