It means the person did the sort of squint that persons do when they are worried, causing wrinkles in the skin around the eyes and probably also in the forehead. It isn't talking about the eyeballs. It is talking about the skin around the eyes.
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"His eyes crinkled worriedly"
This is a poor sentence in a couple of respects. First of all, you're right--"eyes" can't crinkle. And we can't assume anything else but what the writer has written. We may understand what the writer is trying to say, but the writer is using poor grammar to say it. Also, the addition of the adverb "worriedly" is giving the reader an extra clue, just i