How did 'purchase' evolve to mean 'firm contact or grip'?
Could it be as in when you purchase goods, you are bringing them to you. Thus when you pull on the rope, you are bringing the anchor to you. The idea of drawing near makes the meaning similar?
Perhaps the idea of "gripping" something was taken from gripping the rope rather than just pulling the anchor towards you?
I also agree with the other person who said, "chasing the anchor end of the rope".