The cats come randomly, and the most you can do when they come is take a picture of them and collect gifts after they leave. Even if you check the game many times a day, it doesn't take up a lot of time.
Despite having in-app purchases for gold fish, not buying gold fish with real money doesn't prevent you from enjoying the game. Cats leave you both silver and gold fish as presents, so all parts of the game are accessible without spending real money.
After visiting some number of times (seemingly random), each cat will leave their unique memento. You can keep track of the mementos you've collected, but there's no way to use them in the game.
Many new cats and items have been added since the release that usually have their own themes, and it doesn't seem like the devs will stop adding new things just yet.
There seem to be parts of the game that get unlocked as you play more, but you don't realize those features exist until they're unlocked, so there's not a lot of motivation to keep playing the game in that respect. For example, once you expand your yard, you unlock yard remodeling. However, it's not immediately apparent that the remodeling drastically changes the orientation of your yard, or that they may or may not increase the size of your yard.
Depending on the Pokemon one picks for their team the player is able to mix and match in order to plan ahead for what type of match they will be up against. Sometimes this takes a bit of trial and error but for the most part is a deep way to add strategy to what is basically a match 3 game.
Originally this free-to-play title was released for the Nintendo 3DS but has since been ported to mobile. The port offers better graphics over the original due to the game now being able to be played on stronger hardware with higher resolution screens. The graphics are all high res now and look quite sharp.
Nintendo often has giveaways and events that allow players to gain hard to get Poekemon. Users who have been playing since the release of the game will have a slight advantage by having these hard to gain Pokemon on their teams, which for new users will be a bit of a hurdle for multiplayer and single player.
The way the game is made is similar to unlocking new objects in an animation, which is the same for everyone. Kinda makes it feel pointless since you could just google the animation and save yourself like a year of hard work.
Even though your cats bring you money which you can then exchange for special gems, new rooms and new cats cost a lot. It takes ages to collect all cats in all rooms unless you buy the gems with real money.