According to the documentation, the AppMon server (as of 6.5.14) will work with Windows Server 2016 but the DT Collector currently goes up to 2012.
Yes, I concur. I am planning to upgrade my servers from Windows Server 2012 to 2016 at the same time as my v7 upgrade. I knew about AppMon Server being supported, just didn't see anything "yet" about the Collector.
as a rule of thumb you can always assume that every platform supported for the AppMon Server is also supported for the AppMon Collector (but not the other way around!).
in this case it means that Windows Server 2016 was just forgotten to be added to the Collector, too.
in the upcoming release notes for AppMon 7.0 (https://www.dynatrace.com/support/doc/appmon/release-notes/) you'll also miss Windows Server 2016 for the Collector right now ... but that will change until tomorrow or so. 🙂