Yes! The delightful reason why this configuration can repeat within itself is that this Game of Life pattern is a machine with the rules of Game of Life built into it. It's calculating and displaying the game step-by-step. If you watch the machinery you can see the "data" flying around between cells and then the cells turning on and off.
This pattern isn't unique – you could certainly come up with infinitely many more machines in Game of Life that do the same thing. But yes, most Game of Life patterns aren't fractal like this.
This pattern isn't unique – you could certainly come up with infinitely many more machines in Game of Life that do the same thing. But yes, most Game of Life patterns aren't fractal like this.