You can define your fan to be moving space and the pushing of air is the side-effect.
What poster above meant is that wifi is electromagnetic waves, so it does not care whether air is present or not. Air does not significantly hinder the propagation of electromagnetic waves. What you could do to speed up your wifi, in theory, is to fill your living room with argon. Argon has a lower refractive index than air, so the waves can travel faster. The downside is that you won't be able to breathe.