NamelessMC

Which operating system on the VPS are you using, and in which folder is Nameless installed?

CentOS

/usr/share/nginx/html/

I managed to solve it, but now when I go to log in to the site it tells me error 404

I reinstalled the server, and it tells me in General Configuration: Important!

The server must be configured correctly in order to function. To check whether this option can be activated, click here.

To get install.php working, I did this command chmod -R 777 /usr/share/nginx/html

777 permissions are not typically recommended as they open the files up to any users and groups on the CentOS system.

For installations within /usr/share/nginx/html on CentOS, the following should work, although this can change depending on your particular setup!

chown -R nginx:nginx /usr/share/nginx/html

The chown command will change the ownership of the files to nginx so it is able to write to the files as required.

Nothing has changed

In fact, I have now returned to the error 

The website directory or a subdirectory is not writable. Make sure that all files and directories are owned by the correct user.

Example command to change the owner recursively: sudo chown -R www-data: /usr/share/nginx/html

Please research online how to set correct file permissions for nginx on CentOS - if the above command does not solve the problem then unfortunately I do not know what the solution is.