There are screw extractors for wood which you can purchase. They're usually either tiny hole-saws that remove the screw and a small amount of wood around it or fluted bits that attempt to grab what remains of the screw. The latter is very hit or miss in my experience. In either case you'd need to fill the hole afterwards, potentially with a small dowel if using the hole-saw types, and re-tap the hole with a bit.

I've not had to remove a broken screw from anything that has art on it before though so someone else may have a less intrusive suggestion.

Make sure there's not a T-Nut on the bottom of the playfield that the screw went through. I can't tell from the photo if that is just a wood screw or if it goes all the way through . If there is a T-Nut, you should be able to pry that off, bringing the rest of the broken screw with it.

Chris

That was going to be my suggestion too. I think the screw below is a T nut since it is counter sunk for the inlane. Go slow if you take that one off too in case the same thing happens. If either or are wood screws you can convert with a T nut. Just make sure to take out any lighting inserts under the playfield before you do any drilling.

Since the ball bumps into that missing post a lot you might lose more wood from the playfield if you try another wood screw there.

Get woodcraft screw extractor

You can remove it from the bottom of the playfield

Plug hole with 1/4" dowel slice

Re drill pilot hole and install new post screw.
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Glad I could help?

How can you accurately figure the location from the bottom if the screw does not go all the way through the playfield?

Tap broken shaft with a punch or Nail Set, it will dome on the backside of the playfield.

I would get the screw extractor as was mentioned, drill it out from the top (blowouts can be ugly) so you are properly centered. Clamp a block or hold tightly to underside to prevent blowout there as well. Replace with a T-nut / correct screw and done.

Those are nice. I think I'll get a set right now.

If the screw broke off 1/2 way below the surface, you only have to run the extractor 1/2 way through the back.