I need some help here

I think you can report the person for not activating the gift. But I think it will be wise to just tell him to activate the gift.

source: FAQ

The winner has not redeemed my gift, and I'm unable to get into contact with them. How do I proceed?

If you've been unable to reach the winner of your giveaway using e-mail and Steam after seven days of your giveaway ending, and they have not yet activated or redeemed any keys or gifts you attempted to send, please contact support to request a new winner. When creating a ticket, we ask you to include data that suggests you made an adequate attempt to contact the winner, such as screenshots of e-mails, friend requests, or gifts pending on Steam. If the request is approved, a new winner will be generated by the site.

It's a DLC, how do you even check that?

Tell them they must activate the gift. If they don't, report them for inactivated gifts.

Or, alternatively, just report them. It isn't your responsibility to remind others to adhere to the rules, although it's a nicer gesture than to report without first checking if it isn't a misunderstanding (the winner may have forgotten). :P

it's not your problem, it's his problem.
if supports find out the gift isn't activated in his account, he will be suspended.

winner has almost 600 hours in payday 2, i think it's safe to assume he will activate and play it