Normally, when you play and win a game with any deck from the Starter Deck Duel event, you gain those cards from the deck in your collection. Right now it's bugged and not adding the cards. From the latest patch notes:

In addition to the new decks, players will also have each of the current new player deck cards added to their collection. (NOTE: We've discovered some bugs with this that we're working to address)

See the recent patch notes for more info.

I believe you can open a support ticket to get the cards added, and I also think that if you have previously won, then the cards will still get added once the bug is fixed.