Source of Arthur Samuel's definition of machine learning
The exact quote exists in neither the 1959 paper nor the 1967 paper (second version).

These are the closest quotes from the 1959 paper:


  A computer can be programmed so that it will learn to play a better
  game of checkers than can be played by the person who wrote the
  program.


And 


  Programming computers to learn from experience should eventually
  eliminate the need for much of this detailed programming effort.


Also, Wiki page of Arthur Samuel states that:


  He coined the term "machine learning" in 1959


and references the 1959 paper.

Either the quote is created as a gist of Arthur Samuel's 1959 paper, or it is said but not written by him. In my opinion, the former is more probable, since it is not even remotely mentioned in the 1967 paper.