True. Chat bots supply some of the functionality. In Wave you could have bots which would replace, alter, or add content based on things you typed in or some other rules. Like you could have a stock ticker bot, or one that inserted maps, or ones to do live translations.

The collaborative document editing in Google Docs improved afterwards, the Google Wave wikipedia entry doesn't mention this but I have some vague recollection of some of their work being migrated into Google Docs to improve it in that regard. That may be completely wrong though since I can't seem to verify it.

Indeed, and the technologies developed there made their way into Slack, Google Docs, GMail / Inbox, and a bunch of other products.