You can use $variable['attribute_name'] to read the attribute data and for elements with dash and other characters in between the letters you can enclose it with braces and single quotes like I have done for the operating-systems element.
<?php
$url = 'http://www.shinyloot.com/feeds/games_on_sale';
$xml = simplexml_load_string(file_get_contents($url));
foreach ($xml->games->game as $game)
{
    $operating_system = array();
    foreach ($game->{'operating-systems'}->os as $os)
        $operating_system[] = $os;
    if (!in_array("Linux", $operating_system))
        continue;
    echo "Title: ", $game['title'], "\n";
    echo "URL: ", $game['url'], "\n";
    echo "MRSP: ", $game->mrsp, "\n";
    echo "Price: ", $game->price, "\n";
    echo "Discount: ", $game->{'discount-pct'}, "%\n";
    echo "Cover Image: ", $game->{'cover-image'}, "\n";
    echo "Header Image: ", $game->{'header-image'}, "\n";
    echo "Available for:\n";
    foreach ($operating_system as $os)
    {
        echo $os, "\n";
    }
    echo "==================================================\n\n";
}
An alternative way would be like this:
$operating_system = json_decode(json_encode($game->{'operating-systems'}), true);
if (!in_array("Linux", $operating_system['os']))
   continue;
Basically it transforms the result in JSON then convert it back into a simple associative array.