@Martin: there is a workaround for the [fen] sections in the last version of RPB Chessboard. But [pgn] sections still do not work.
@Robin W: thanks for your answers. The “bbPress – Do Short Codes” plugin do the job.
However, there is still a problem: bbPress seems to have a kind of postprocessing that adds several <p></p>
tags within the post content, including the sections that result from shortcode processing. Is it possible to disable this behavior?