You're including HTML inside the php (<?php ?>) tags. Any HTML needs to be outside the tags or echoed inside.
*EDIT*
You still need to echo your PHP var for it to evaluate inside the html. For instance, use short tags for this:
<param name="movie" value="games/<? echo $game; ?>.swf">
*EDIT*
You still need to echo your PHP var for it to evaluate inside the html. For instance, use short tags for this:
<param name="movie" value="games/<? echo $game; ?>.swf">