Directly from the email (I added the bold print)
"...FREE to anyone who logs in and plays World Golf Tour today..."
Yes, you must play.
I linked in from the email, logged in and played a CTTH tourney within my CC. I didn't receive the golf ball so I simply contacted WGT through the link provided at the bottom of this page. I'm confident the situation will be resolved so there is no real reason to complain about it here before they have a chance to deal with my direct contact.