The 'thrill of the chase' refers specifically in a figurative way to the thrill that guys feel ,when hunting girls.They seem to love the hunt ,pursuing an unattainable goal of getting a girl ,who doesn't seem that accessible.

It refers to two things: 1. Fox hunting 2. Skirt chasing I think you get the picture.

It can also refer to hunting , where men like to hunt animals, but once they've shot them, they just pose by the dead animal, have a photo taken ,then go on to hunt the next animal.

It means the excitement in pursuing something - as opposed to the thrill of actually catching it. An example would be a man that loves going after a woman, then loses interest in her once she accepts him.