The character named Shigeki is a shogi player. If you're unfamiliar with the game, shogi is similar to chess. A couple of terms pop up in this ep directly relating to the game.

17:45 - 3-dan is Shigeki's current rank. It's not exactly a low level, but it's lower than he would like, which is why they call him "3-dan" as a teasing insult.

17:56 - The Shoreikai is an organization run by the Japan Shogi Association that trains professional shogi players. A similar organization exists for go (which you see in Hikaru no Go).

If you wish to learn more about shogi, you can read the rules at this web page.