@Bartude, well in this case and only because you do not want to use laravel passport as @Hawkleaf has mentioned. His is still the best long term advice and someday you will have to use laravel passport.But with your current comforatiblity at scaling your app, I think that @Borisa has the best answer for you. Build it as one application and route to the different games. So in essence a single app, that with a solid folder structure to your games, because you can have many controllers and models and everything you want in one application, while still having a seperation of concerns. While still in development mode, If you are not yet comfortable with having all that logic in one place, do it as you are doing it, it will work connecting your single database to all the different projects, but remember that each project works on its own, the only common factor is the database none of its logic. Each game will have its own logic. You will have to rewrite a lot of the same stuff for each one, that is the problem!
But you will learn how and what to build for each game.
My advice is to start with the games, each as a project so you can mess up and change things to get it working to your requirements, then when you have those in place.Start working on a single application that has the login and Home and all the bells and whisles, then you can start by implementing those games you already have the code for to your application.
In the process you will learn a lot about what works and what doesn't and the fallout is minimum because you are isolating the projects.