File permissions for SQL Server 2014 virtual account
Dan,

I'm assuming the account running the agent job is a sysadmin. In this case, the
DEV instance will need to have its' service account or service sid for the DATABASE ENGINE given access to the folder.

SQL Server agent doesn't do the restore, it connects to SQL Server and impersonates the account if non sysadmin and then continues. In this case you're connecting to the database engine and issuing a RESTORE DATABASE command which will be processed by the engine. SQL Agent isn't touching the backups, the engine is.

Edit: Explaining the posted agent output

Executed as user: NT SERVICE\SQLAgent$MyAppDEV.


This is letting you know that the Agent job was executed as the SQLAgent$MyAppDEV local account. This is most likely due to the job owner being sysadmin.

Cannot open backup device 'E:...MyApp_backup_2016_02_24_092912_0136837.bak'.


Here is the actual error, we can't open the file. We don't know why yet.

Operating system error 5(Access is denied.).


This is explaining why we can't open the file, the OS returned error 5. This can be validated by checking the OS return code by executing net helpmsg 5 on a command prompt.

[SQLSTATE 42000] (Error 3201)
RESTORE DATABASE is terminating abnormally.
[SQLSTATE 42000] (Error 3013).
The step failed.


Some extra notes about what is happening, but this isn't relevant to the actual error or issue.