The screenshot you showed had the search term right in the tweet.

I just did a Google search for that same term, and no Twitter-formatted results came up, though I have seen them before. Looks like Google is playing with it at the moment.

It certainly isn't arbitrary when the results show up.

As to how to get placed and the like, who knows at this point. Your Twitter activity is public, and there are only half a jillion services crunching them to tell you something about how well you tweet, so I wouldn't be surprised -- no, I'd expect -- that Google's working on its own algorithm. Call it "Google Tweetrank" and expect that it will be open to wild speculation like everything else that Google does.

Should you include keywords, hashtags, etc., that you want targeted for search? People do this already, but if you go overboard you're eating into your 140 characters and your followers will get annoyed and feel like you're placing SEO over interactions with them. (Or not. I don't know everything about Twitter.)

I have heard that Google is revamping their algorithm overall to include many new things to include and to begin excluding other criteria that was once highly important.

They will continue to do this until they, Google, gets it right in their eyes :)

As for me I try to keep everything in terms of keyword without compromising my "tweets" or any other content in the social media. Just keeping to a simple rule of thumb and connecting all the dots within your business marketing will generate Google results which will eventually include, tweets.