It does not insert a meta tag for the "focus keyword".
According to my understanding of this article, the keyword focus is just the keyword that you target in your content. You modify the "keyword" by modifying your content. The Yoast tool just helps you identify what this keyword could be and how to achieve it (by modifying your content).
In itself, the Yoast tool does not do make no matter what.
Because the Meta Keyword tag is no longer used by Google.
Yes, there is no "magic" tag that identifies the keywords. Google analyzes your page contents identify the subject (and the keywords).