You probably didn’t see the the in-forum documentation about Plex on DSM 7.
A lot has changed and it’s about to make one  final change.
 final change.
Since you have a new installation on DSM 7 (no previous data), the easiest procedure will be
- Uninstall the DSM 7 package + ERASE option (remove that server data)
- Create a shared folder named “Plex” (capitalization important)
- In that shared folder, create folder structure
Library/
  Application Support/
    Plex Media Server
- 
Now you place all the files from the shield (preserving directory structure) from its “Plex Media Server” directory into the corresponding one above on the Syno. 
- 
When all data is transferred, you can Manual Install the package you downloaded from https://plex.tv/downloads and begin the “migration” process. It’s detail rich because of all of DSM 7’s limitations but if you take your time, it will work. Most important is: Once it starts “Installing” — let it run until it completes. 
Here is the documentation which details the changes DSM 7 brought (not our choice) and what to expect to get the data into DSM 7.
There is a change coming which makes a lot more sense because more information is visible (e.g.  a PlexMediaServer shared folder as prime example)
If you wish,  since this is happening very soon,  you can use it now if you wish .
I have released some “Forum Preview” packages in this new structure.
What you gain is you’ll start out in what will very soon be “production configuration”.
The choice is yours. Please advise.