It's not possible to enter a DLC giveaway when you don't own the base game.
I don't think it's possible that the winner of the main game can win this one, both giveaways end in the same minute and the winner can't enter until they retrieved the key and redeemed it and the Steamgift site has re-scanned the library to confirm the winner redeemed and owns it.

HowDareYou to gift me this nice dinosaur pack? Uh? ^_^
Thanks for the nice surprise. Honestly, JWE is not too high in my playing priority list, but I know I will eventually play it a lot because it's a great mixture of many things I like: management, building, artificial life sim and... Dinos!
You don't seem very active, but still welcome to my whitelist. Have a great weekend!