The next step (a toughie) is to ensure Single-Sign-On (SSO) so that the Moodle user can login automatically as a phpChess player.
What you are describing reminds me of the Conditional Activities in Moodle 2.x. And it can act as a motivating factor for the chess-playing student to complete his online homework/assignment on time so that the user can enjoy some games to improve his or her PhpChess rating.
Which begs the question: what about the non-chess playing Moodle users?
Your ideas will be useful for a chess learning online course.