Why do some oil heaters ("red diesel") use also electricity and some not?
The Webasto-type heater uses a high-pressure electric pump to atomize the fuel, and an electrically-powered glow-spark plug to preheat it.

The burner your link points to is a gravity-fed burner (i.e. there is no electric pump). It exists in two variants:

1- yellow-flame type = a less efficient, but less complicated system.

2- blue-flame type = a more efficient, but more complex system. The blue-flame system works like the multifuel expedition stove: after a period of preheating, the pipe bringing the fuel to the fuel jet becomes very hot, so the fuel it is transporting vaporizes; the pressure of the gasified fuel rises, and the resulting high-pressure gas exits the burner jet and combusts with an efficient blue flame.

The latter system thus requires no electricity, but needs a brief preheat period to begin working. During this time the flame is yellow, and may produce some smoke.