Google gets to know a user's IP when someone enters a captcha even if they are using tor (see http://www.wired.com/2014/12/google-one-click-recaptcha/). So, If I go to a non-google website, such as cnn.com, and it asks me for a captcha for submitting a particular form, will it hand over my IP to cnn?
CodesInChaos is correct.
When you visit a website they can view the IP address you connect from. That is how Google views your IP address, as for the captcha your browser connects to Google's servers. When you connect to a site they can see your IP address, regardless if you enter a captcha or not.
As per @CodesInChaos comment:
Google gets to know a user's IP.Citation needed
Nothing in the article you linked indicates that Google learns anything except the exit node's IP, which the webmaster can see without involving google.