Chinese characters are mostly complete words unto themselves. There are some characters which signify a sound, not a word, but by and large most characters have meaning.
This leads me to ask:
How does one play Scrabble in Chinese?
We play scrabble by building on letters in one word to spell another word. If each character is already a complete word then we can't build on it. True, we have compound words, but those are usually composed of two or three characters (telephone is made up of the two words "dian-hua," or "electric/electricity-speak/language"). We could play by transcribing words but we'd have to find a way to include tones in our writing.
The question popped into my mind as I was on a late night stroll last night. Now I'm curious and am going to have to find out.