True - they're indispensable. I have a coworker who plays Scrabble at a competitive level and has memorized every 2, 3, 4 and 5 letter word in The Word List, and will randomly shout out, on hearing words like "tandoor", that there are 3 anagrams of it - tornado, odorant, and something else I can't even remember. It's an amusing parlour trick, but seems a very arbitrary, non-transferable skill he's developed.
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.