The system service port that RobotStudio emulates is always changing, not the 80 in the documentatio

You are at the right place, you should modify appweb.conf. But you have mixed things up a bit. 

Listen -1 ==> Is for HTTP connection. Defaults to 80 if you don't have any server running on localhost port 80 that interfere then it will assign a random port. If so the specify the port manually by exchanging -1 to the port number you wish to use instead.

ListenSecure 666 ==> Is used for HTTPS which normally uses port 443 not port 80. Using -1 here will result in a random port assignment so specify the port you wish to use here (not port 80). 

TL;DR

For HTTP:
Change "Listen -1" to "Listen 6767" to have the VC always listen on port 6767.

For HTTPS:
Change "ListenSecure -1" to "ListenSecure 6767" to have the VC always listen on port 6767.