Kisshomaru, good, you got your site working.
For others, the “Giving WordPress Its Own Directory” page covers how to move most of the WordPress program files, while keeping, as Ron says, index.php in the root. And that works just fine; URL would be like yourdomain.com/index.php (or https://www.yourdomain.com/index.php)
Since the URL doesn’t change, with that you can use domain mapping.
What doesn’t work, when we say “to use domain mapping, WordPress has to be in the root of your account or the root of a subdirectory”, is having the URL to WordPress be something like yourdomain.com/wordpress/index.php
There is a section on the “Giving WordPress Its Own Directory” page that won’t work (Ron, correct me if I’m wrong, I haven’t tested it) with domain mapping. Section titled “Pointing your home site’s URL to a subdirectory” for use e.g. by organizations hosting a yearly conference, so the URL shows visitors the 2014 conference then the same URL shows visitors the 2015 conference.
The multi-site way to do that would be have one domain name for WordPress administration (e.g. mywordpresssite.com), have another domain name for the conference(s), use domain mapping to map myconference.com to conference2015.mywordpresssite.com and then for the next conference simply redo the domain mapping. (Can you have site names start with numbers, e.g. 2015? Either test thoroughly, or simply start with a letter…)