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Since they introduced the square-selecting captchas I have always assumed that they use it for identifying the user. I bet that depending on how you solve the captchas they can identify who you are if their system already has a theory of who you might be.

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they're there for denying access to automated scripts.

This is the reason they exist in the first place, but doesn't answer the question why they're implemented this particular way.

They're implemented this particular way to provide training data for image segmentation systems, they move the image around inside the frame which allows them to use a few people doing the challenge to create a boundary representation that can be used to train things like YOLO style ML systems

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