To play the card game in the Lounge Area, you will be rewarded with the Lounge Cards producer for one of the tasks. Once you tap on it, it will produce cards.
To play the game, you will see certain cards that you need to merge up to. Using the Lounge Cards producer, you need to spawn cards (they will come in different colors, numbers, and types) and merge them until you make the necessary ones - when you do this, you will be able to complete the task and get the task rewards. Keep in mind that only cards of the same type, color, and number can be merged to create higher-level cards.
Additionally, you might also get a Joker from the Lounge Cards producer - this special card can upgrade the card of your choice to the next level!