Logic #1 is checking the returned value of the preg_match function with respect to 0 and with operator ===. That means the returned value of the preg_match function has to be (int) 0 or (string) 0. And after that it is checking if $_REQUEST['author'] is empty or not.
And in Logic #2 is checking the same thing above, but with !()(not) operator. And this method also additionally check the $_REQUEST['author'] is integer or not.
Checking the $_REQUEST['author'] data type actually makes Logic #2 better than above Logic #1, I think. Cause, though data type doesn’t matter in PHP (PHP is a loosely typed language) but it’s better to use them. It defines a concrete base for your application and ensures some core security as well as it’s the best practice.
Hope that answer satisfies your quest.