"Add game to my library" button, on item I sent to someone else

My experience has been that if the gift is still in the sender's inventory, then the receiver hasn't clicked on the email link and chosen to add it to their library or inventory. So technically I think you would be able to add it to your account unless what you're experiencing is a Steam error (entirely possible - we know how Steam likes to roll). Whether you should or not... I don't know. If he planned to re-gift it or trade it, he would have been smart to add it to his inventory rather than leave it in limbo.

He hasn't accepted the gift

When you send a gift to someone's email or Steam account it will stay in your inventory until the recipient accepts the gift (once he accepts it he can choose whether to add it to his library or keep it in his inventory). Only when he accepts it, it will disappear from your inventory.

So if it's in your inventory, that means he hasn't accepted the gift yet.

He might have marked it as received because he'd saw the email and he might have thought the DLC would be automatically redeemed on his account. Some people think that as they got an email coming from Steam they would take care of that and they don't realise they still have to accept the gift themselves.

My advice is that you contact him again telling him to search for that email and accept it. If he can't find it or if you want to re-send it so he doesn't need to dive in tons of old emails, sending it again to the same email won't work, he won't receive a new one and that will make the previous email invalid. Try using a new email address (it doesn't need to be linked to his Steam account) or try adding him to your friendlist.

Cheers! :)