How deep in the Uncharted theme? Is there voice clips? Music? Some kind of rudimentary story?
No story, you only fight the characters of the UC game Universe after one another. They don't really distinct themselves in terms of "character", but more by the gameplay challenge they offer. Drakes first card is always Drake, which is one of the strongest cards in the game, so that makes him different to play than Elena.
I think they also tried to actively avoid scaring non-UC people away with too many tie ins, but at least the cards have some flavor text that is usually a quote by the depicted character. As I stated in the buying recommendation table, it's more important that you can sort of deal (pun not intended) with card games, than having an attachment to the Uncharted Universe.
While I agree that "battling" characters one after another doesn't sound too exciting, the gameplay is really well done and I'd argue that the 5$ price of admission is a great price to find out whether you are still able to like card games these days or not.
So glad they chose the base game + DLC model tbh. I feel that 5 vs 10 bucks for the initial investment would make a huge difference for people just checking out the genre. they know too well it is quite the niche genre. Makes it a whole lot easier to recommend to others.