Before discussing the electronics---do you understand that turning on an electric fan does NOT lower the temperature of a room? If a room is at 40 degrees (Celsius) and you turn on a fan, the room remains at 40 degrees. It may feel cooler because the moving air helps evaporation of perspiration to cool the body---if the humidity is significantly less than 100% so that perspiration can evaporate. But the point is, in order for a room to feel cooler (not be cooler), there has to be someone in the same room as the fan. Otherwise, the fan is moving air around without any benefit to anyone (or anything).
I'm straining my brain trying to figure out why you need a wireless sensor to turn on a fan up to 2 miles (or even 200 meters) away from a hot room (or patio, or wherever it's placed), and I can't think of a single application.
Since the fan needs to be in the same room as the sensor in order to give any comfort, why not just use a sensor with an on-board relay to switch line power (220 VAC)? I'm pretty sure such a local thermostat costs a lot less than the $200 price tag in your link.