The idea is really cool, but i did have some trouble progressing through the early game, where your money generation is pretty low - this is turned into a bit of a slog with the speed of the AI animations (it might be helpful if there was a speed up button). I found that the best approach was to select random cards in the memory match, end my turn, then return to the main menu with my 1 gold for ending a turn, avoiding the time needed to wait for the AI turn.
Overall though, it's a really interesting idea, and I'd love to see more expansion into more games (especially the memory games, which can be kinda tricky when you have to keep track of multiple boards at once), and items that provide interactions between different games (ex. rather than giving an extra turn in another game, perhaps placing down a piece in Connect 4 - essentially, you'd have to think about how each move affects other games)!