These are the only two games in the arcade, you can also play in Gourmet Street and Toy Land.
You can have more games either connecting your device with Meets stations (they are only in japan, and not sure if it can connect with Tamagotchi ON)
Another way is if you download and install a fan made app called MyMeets where you can access to all station content and have them in your tamagotchi. But you might face some issues as it’s not an official app by Bandai.