First off, try echoing $query. I predict that will yield your problem.
Also, you may try this...
// setup a query variable to ask the database for some information
$query = "SELECT * FROM $action_games ORDER BY gamename";
// acctualy ask for the info & store it in $results
$result = mysql_query($query) or die("Could not store game info in database results.");
Now maybe not using the "." is just my programming style, but it works. The beauty of php 🙂