Bob Toski believed that the way to learn the game was from the green back to the tee. He felt that you should learn to hit solid putts, then solid chips and pitches, then short wedge shots, gradually working your way back to the driver. Learning this way teaches you to learn how to make a solid strike and helps you develop feel before you try to use the big dog.
The chip shot is indeed a short version of the full swing. I have found that hitting my approach shots thinking of them as long chip shots has really helped my rhythm and my striking. I have also found that this kind of thinking helps in shaping shots. To hit a draw, I think of the strike like a running chip shot. To hit a fade, I think of a pitch shot.
The bottom line is, if you can learn to chip, you can become a good player. The chip shot is just a shorter version of the golf swing or vice versa. You can build your golf game around a solid chipping game. Learn to chip, then remember that the full swing is just a long chip shot. No need to muscle the ball. Just chip it.