How can I add a taste of adventure games to my game?
This is an interesting scenario. The first idea that sprung to mind would be to have a set of cards that relate to each other specifically. Each card in the set needs a certain criteria to be met to allow you to then search the deck for another card in the set. The harder the "quest" is the more cards there are in the set that you need to complete the adventure. 

On reflection, this seems more like a lore issue than a mechanical issue. The wording on the "adventure cards" may be the best place to include your adventuring aspects. Maybe have "Scenario" cards that explain a certain journey and need choices to be made at certain points (Maybe drawing from two separate decks that accompany the scenario cards?). These choices determine the outcome of the adventure.

This is only a brainstorm. I'd like to think I could come up with more ideas. If so I will update the answer.