Mini Games exist in virtual worlds as they are on the main functions of an online games economy. They are a way for users to earn points, and they are a way to bring points out of the game's economy. Especially depending on if they have point sinking features as well with luck/chance games.
Without mini games in the pet game, it will be pretty difficult to build a game's economy, you actually need them to develop the game's economy from the ground up.
They also enhance the game's appeal as well. I would honestly say, this was probably one of the things that main Neopets a big success story back in the day too. They had a ton of games to play in the early days and still do. Marapets also a wide variety of games to play, and their economy is quite strong too.
Mini games also keep users entertained and keep them on the game longer, which is a great thing. If you want your game to have more sticky value and more entertaining value, games tend to keep that appeal for you.
However, some games can go without mini games depending on the functions of the gameplay elements itself.