At the end of the article, why is apache even being used anymore?
Just use nginx and php-fpm (or php-cgi/fcgi).
Just use nginx and php-fpm (or php-cgi/fcgi).
Are there any performance benefits to having Apache as well?
The only benefits I can think of offhand would be if you had a requirement for something that Apache specifically provided, or custom modules you needed run. Something like suphp, modsecurity, or shared hosting configuration, etc. All policy type stuff, not performance.
In fact by not using PHP-FPM you lose out on awesome stuff like the slow log!