Looks like a cPanel clip.
There could be other error logs which don't combine with litespeed's logs.
CentOS 7 but with 'cloud linux' ... so it's not 'stock' CentOS 7. I've got a couple of 'stock' sites and don't have the issue.
So what other protections does your server have?
One of the things that causes issues with CentOS 7 sometimes is a thing called 'seLinux' ... security enhanced ... it might not log errors to Litespeed logs but to logs of it's own.
Typically, if one had root access to server (which you shared with me in a PM you do not, and you are acting as a go-between to those who do), a command exist to see if seLinux is set to enforcing.
Your server might also have other protections ... like apache's mod_security, or securi or suPHP or ????
Basically, when moodle attempts to generate a png image of whatever is being converted, it relies upon ghostscript (gs) to do that ... the path you enter might show a 'check' ... meaning it found gs at path given, but that won't tell you if Moodle can actually run it ... in your servers case, Moodle code can't - we've proven that.
Why do I get the feeling am trying to teach your hosting providers tech support via proxy (ie, you)?
Maybe, hosting providers tech support should join the forums - if they are gonna tell customers, ie, you, their servers can run moodles, then it suggest they have some knowledge of moodle.