No idea, really. The file is written using a very standard PHP-function (file_put_contents) like this (from autoptimizeCache.php on line 52);
file_put_contents($this->cachedir.$this->filename,$phpcode);Based on the warning you see, the error (which clearly states permission is denied) seems to stem from "something" in /nas/wp/www/common/production/php_prevent_flock.php on line 21, which is not part of autoptimize.
What is even weirder; I have other users on WP Engine (example here) who are able to use Autoptimize just fine.
Conclusion; I really have no idea why it doens't work, but I'm pretty convinced this is not a Autoptimize problem.