Does God only work through Magic?

[Nope]

Yes, a deity could work the way you describe; however, it would seem silly/cruel of him to expect that people worship him under those same conditions. In your analogy, the pianist isn't expecting the mice to worship him. You can make a case for a deist type of god that leaves his/her creation alone after setting things in motion but it is a big jump from there to the type of god described in Christianity.