I would say yes, that’s the problem. If on your machine, the project used a database, then you will need to provide a database for it to work .
Now that I’ve read the tutorial, it actually mentions that you need to change the database credentials (though for some reason he says it’s optional, where I cannot think of a Laravel project that doesn’t use a database).
Finally, you can deploy your project to Heroku, which has a free tier far better than a shared hosting. Then there are the cloud providers that offer a 12 month free trial (google cloud, amazon web services and Microsoft azure).