You used to be able to dial TIM on a landline phone to check the time (for free?). Then you (if you were a computer nerd) checked it on your computer, then on your cellphone. Because that's what was available. There was no connection between knowing the time and landline phones - people just had landline phones so it was a convenient way to deliver the service. That's how it is with mobile games now.
Remember Java and Flash applets? You could make anything you wanted as a native application, but RuneScape took off because you didn't have to install it.
The "big family computer" became an iPad.