MapPoint® 2016 was never released. The last version of MapPoint was MapPoint 2013. There is one suitable desktop replacement for MapPoint 2013.
Maptitude is feature equivalent to MapPoint and supports MapPoint files
Imports MapPoint PTM files
Unlimited layers/geocoding/routing
Radius and drive-time tools
Demographics
Routing tools
Export to Excel
Link and update data
Copy drawing items between maps
Territories