When you see Permission denied, that should be an immediate indicator that file permissions are not setup as you need them to be. Shiny Server runs as a configured user on the system (usually shiny). That user needs to have read (and sometimes execute) privileges on the files in question.
The rest of the error message usually gives you a little bit more context. As we can see:
It looks like file privileges on global.R make the file not accessible to the user running processes on Shiny Server. Again, this will depend on your configuration, but it is the shiny user by default, I believe.
If you want to do more in-depth testing, you can assume the role of the user in question (i.e. sudo su shiny) and then try to execute the app / read the files / etc. Resolving the issue will just be a matter of setting the UNIX file permissions so that the files are readable (or writable / executable as the case may be).
A simple tutorial on UNIX file permissions