Sigh?
The issue was a javascript problem...not PHP. You had too many double quotes...I'm adding the returns so it doesn't fall off the page...normally javascript won't like this so I don't recommend using returns in your code...
print("<a href='#'
onclick=\"window.open('/match/view/view.php?match=$Challenged[Match_Id]',
'NewWindow',
'toolbar=yes,location=yes,directories=no,status=no,
menubar=yes,scrollbars=yes,resizable=no,copyhistory=yes,
width=635,height=260');return false;\">$Challenged[Match_Id]</a>");
It's certainly messy and not the most 'readable' code, but as I pointed out, the problem is not PHP, it's javascript and quotes issues (you'll see where I \ the double quote for javascript (which PHP happens to appreciate as well)...