As for 'learning new words and their meanings', clearly Scrabble isn't that game. But to be fair that isn't its stated aim, either. If you know any good examples I'd love to play them.
He also has a couple of funny anecdotes about words that aren't allowed - like "picowatt", which rather offended our collective sensibilities as electrical engineers.
You're quite right that Scrabble is not about definitions, per se. But Scrabble does describe itself as a "word game", and it really isn't - it's more of a memorization with a bit of math kind of game.
Awesome project @zephod!
On the other hand, crossword puzzles are single-player games that use natural language wordplay to create a challenge. Some AI work has been done in this field, which can use a Web search engine (like Google) to try and determine the answer to each clue based on the clue (as well as any candidate words/letters already filled in). The hard part is understanding the clue. Look to systems like IBM's Watson to see how those kinds of problems can be solved.
"Solution" in a single player game, like a crossword puzzle, is solved in exactly one way: when all the rows and columns are filled with legal words (usually -- unless the author rigged it to allow clues to have multiple solutions, like the election day crossword in the NYT in 1996). A "solution" in a two-player game is when, no matter what move you make, your opponent knows perfect play. For example, checkers is solved: http://en.wikipedia.org/wiki/Chinook_(draughts_player)
I guess it's kind of like chess: it's almost impossible to beat a computer, so it's effectively solved. Except when they play each other :)