No, that’s coaster brakes, fixies are different.

Coaster brakes allow you to stop pedalling and still move forward woth your inertia. In fixies you can’t stop pedalling otherwise you would be braking.

The image is funny cuz if you are gonna add a hand-brake, makes way more sense to put it in the wheel axle instead of the pedal axle cuz you are still straining the chain.