Piecemeal restore only one filegroup without primary filegroup restore
You can't restore a file or filegroup without restoring the PRIMARY filegroup. There are a number of reasons for this given your scenario:


Under SIMPLE mode, a Partial Backup always contains the PRIMARY filegroup and all read/write filegroups. You would need to switch to FULL recovery to utilise file/filegroup only backups that can exclude the PRIMARY.
If no PRIMARY filegroup existed, the system tables and metadata for your database would not exist, so no database users, no schema information, nothing that SQL Server needs to know about your data, files and filegroups would be available.
Under SIMPLE, no log backups are taken, so you cannot replay the transactions against the non-PRIMARY read/write filegroups meaning they must be restored from a backup consistent with PRIMARY.


Even under FULL recovery, the primary filegroup must be restored to allow you to restore individual files/filegroups because all the core metadata about your database is there.

The idea of Partial Backups and Piecemeal restores is to allow you to get back online in a disaster quicker by restoring the essential filegroups needed for the database to be operational, and you can restore additional filegroups later.

I would suggest you look at making some changes to your database:


Move all user objects and data out of the PRIMARY filegroup so that restoring it is less time consuming.
Switch to FULL recovery mode and implement separate filegroup backups and frequent log backups.
Mark any filegroups that should not be updatable as READ ONLY.


These change will allow you to simplify your restore process. Assuming you'd made the above changes and wanted to restore the file you've mentioned, the process would be:


Take a tail-log backup
Restore the primary filegroup from backup
Restore all log files with no recovery (except the last restore of the tail log backup, which is done with recovery) (DB is online at this point)
Run "RECOVER" on all the undamaged filegroups (Data in these FGs is now accessible)
Restore the damaged filegroup from backup (DB is now fully recovered)


This would be quicker than partial backups under SIMPLE recovery because the undamaged filegroups do not have to get restored from backup, instead the data files on disk are simply recovered by SQL Server and transactions replayed from the log onto those files as appropriate. If the PRIMARY filegroup is small, and you're taking frequent log backups, the whole process should be quicker than restoring all the read/write filegroups as with partial backups under SIMPLE.