[rum3]

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.

[kmlx]

they're there for denying access to automated scripts.

[pawelk]

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

[faceplanted]

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