Upgrade from SQL Server 2008 R2 Enterprise to SQL Server 2016 Standard Edition?
A quick Internet search for 'sql server restore enterprise to standard' indicates this is 'theoretically' possible if you're not using 'Enterprise' features.  The only way you'll truly know is to actually attempt the restore of a backup from SQL Server 2008R2 Enterprise to SQL Server 2016 Standard.

Downgrade from SQL Server Enterprise Edition to Standard Edition

Migrating a database from Enterprise to Standard Edition