Right, that should work. Remember, headers can only be sent BEFORE any page content. You tried to echo $cnew, writing content to the page, so the header fails.
/* Count How Many Times A Space Game Has Been Played */
$temp = 'usr/local/psa/home/vhosts/gameygro.com/httpdocs/data/gamecount/spacetotal.txt';
$fw = fopen($temp ,"w");
$cnew = $count+1;
$countnew = fputs($fw,$cnew);
/* Send To Correct Page */
header ("Location: /play/space/$QUERY_STRING.php");
If it doesnt work, post back.