If you post a tweet with a link to a Gist on the new Twitter interface, you can just click the tweet to see the Gist in the right pane. I imagine it would be nice to see a person's stream with the tweets on the left and a gist in the right. Especially if it was a daily code tip account.
I suppose you can't see it if you don't have the new interface though.
I believe it's using 'oEmbed' to advertise the excerpt to Twitter -- so other websites can easily export excerpts to NewTwitter's second pane, as well.