I'm a competitive Scrabble player. While you're absolutely correct that learning arbitrary strings of letters is a part of the game, this doesn't imply that developing one's vocabulary isn't.
As a result of the game, I've learned tons of words whose meanings are completely unknown to me (mbaqanga, eolipile, aboideau) and tons of words that have enhanced my vocabulary (prexy, glaire, oomiak).
Off topic, but I can't resist: the (a)eolipile is one of the coolest objects in history. It is literally the first steam-powered machine: http://en.wikipedia.org/wiki/Aeolipile . Its invention suggests that perhaps if things had gone a bit differently the Romans could have made steam power practical 1400 years before the Industrial Age.
As a result of the game, I've learned tons of words whose meanings are completely unknown to me (mbaqanga, eolipile, aboideau) and tons of words that have enhanced my vocabulary (prexy, glaire, oomiak).