It's not necessary, but remember that the less you know about the other aspects of game development, the less "mobility" you have. In other words, the more well-rounded you are, the more marketable you are and can qualify for more positions.
With that said, however, it's fairly common to enter a game development company at the entry level (for example: 2D Artist Intern) and then learn the ropes of the other departments while you work. 2D art/texturing often leads to 3D modeling, leading to animation, leading to environment interaction/design, etc. You become an attractive candidate if you show the will to learn and expand.
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