No, since mysql_fetch_array() is used to place a row from a result set into an array, not execute an SQL statement.
Now, do you need to print the number of logins? If you do not, then your first SQL statement should just select the count, and the second SQL statement should either insert a new row, or increment the number of logins. For example:
$query = "SELECT COUNT(*) FROM players WHERE guid='$guid' AND ip='$ip'";
$result = mysql_query($query) or die(mysql_error());
if (mysql_result($result, 0) == 0)
{
$query = "INSERT INTO players
(guid, name, ip, first_seen, last_seen_date, last_seen_time, logins)
VALUES ('$guid', '$name', '$ip', '$date $h:$m:$s', '$date', '$h:$m', '1')";
mysql_query($query) or die(mysql_error());
}
else
{
$query = "UPDATE players SET logins=logins+1 WHERE guid='$guid' AND ip='$ip'";
mysql_query($query) or die(mysql_error());
}
Incidentally, you may want to consider switching from the legacy MySQL extension to the PDO extension or the MySQLi extension.