Digital video cameras optical zoom vs lenses
Your facts mislead you. Lens magnification and size have nothing to do with video or stills. They have to do with sensor-size.

Your DSLR has a large sensor and requires a large lens. The digital video camera you refer to has a small sensor and requires a small lens. You can very easily pick some random examples to show the opposite! Take a Canon Powershot SX50 HS, for example, which has a 50X optical zoom and a Sony NEX FS100U which has a sensor larger than your Nikon and will require an even larger lens to achieve the same magnification. This makes it impossible to get the kinds of zoom seen on small cameras without the lens requiring its own transport mechanism!