Will a SQL Server 2008 R2 MDF file work on SQL Server 2016 with Windows Server 2016? We release our database as a .MDF file taken from a SQL Server 2008 R2 server. I have a client who is planning to move to SQL Server 2016 on a Windows OS 2016 and is asking if our .MDF can be restored as a database on their SQL Server 2016 and will it work with Windows OS 2016.

I know that SQL Server 2016's lowest compatibility mode is 100 which is SQL Server 2008 but will it work on Windows OS 2016?

This article makes me feel that it wont https://www.sqlskills.com/blogs/glenn/operating-system-support-for-sql-server-versions/
The article you reference merely states what version of the SQL Server engine is supported on the various operating systems.

You should not encounter any problems attaching (you don't restore) your mdf file to the SQL Server 2016 instance running on Windows 2016.  

Note: During the attach, the database will be upgraded to SQL Server 2016 and can never be restored back to a SQL Server version that is prior to 2016.