I wish they would explain more about how the user interacts with the whole reCAPTCHA leads them to know it's a person and not a robot, but maybe they're worried about people writing bots to get around their protections.
Probably using a combination of G+ and GA to check your 'history' to see the activity is like a normal human. Visits a couple news sites each day, checks their gmail, searches for random crap randomly, GA registered a 'conversion' for some company = probably a human
They're almost certainly using the adwords cookies that get hit from 90% of the sites out there to figure out if you're a bot or not.