The earth is spinning like really quickly all the time and we just don’t notice it. Heat if a form of vibration, and so when heat is applied to the bottom of the fan the atoms there move more. A gyroscope resists tilting forces because it is spinning, and the earth is spinning, but the vibration of the fan decouples it from this effect. The blades are able to move freely and the earth moves around them, pushing air through the blades.

tldr: It’s not spinning, you are spinning