Plywood is many layers of wood glued together.

Wood, of course, is imperfect; so if one layer has some checking, it may not bond correctly with the lower ply.

Is that "splinter" loose, or is is bonded to the next layer?

Use some Titebond III glue and fasten it back down.

Use a clamp, so you can apply some pressure. Wax paper between so the clamp does not get glued to the playfield.

Easy fix once you have done one.

The glue dries a tan color, so use your judgment.

If you ever get your playfield clear coated, the restorer will fill the void and paint it to match the surrounding wood.

Press down on the splinter when you first put the glue under it and see how much "squeeze out" you get. You will get a larger squeeze out with a clamp than your finger...