As I know there are big live instances (partners and meta itself) of Discourse at the moment. What is a share of traffic to the site that comes from Google? What should be an expected share after several years of forum existence?
Will any Discourse instance have the same level and share of SE traffic as any Stackexchange site with the same content (for example, if content of games.stackexchange.com is moved to games.discourse.org, provided domains have same rank and trust)?
It will be a lot lower in general, as most forums are primarily social in nature and not laser focused on “turn a practical problem you face into an answerable question, and vote the best answer to the top” ala Stack Exchange.
If SE produced, say, 80% useful search results out of all the pages generated, the average forum (Discourse or not) would produce maybe 10%. And that is probably a generous accounting. Of course this depends heavily on the forum subject and its policies, etc, but on average.
Think of it this way, how many Google searches do you do that result in forum results today? The answer for me is about once a week, maybe a few times a week depending on the searches. Discourse would have to become huge indeed to move the needle on that.