The MTU of 1600 is required where any VXLAN traffic will traverse, usually among VTEPs. If the VTEPs on host A are on a different switch than the VTEPs on host B, and they need to communicate, everything in the path, whether it's a switch or a router, will require a maximum MTU size of 1600.
The NSX Manager and NSX Controllers do not require an MTU of 1600 for communication.
The design guide is a good source of answers:
https://www.vmware.com/files/pdf/products/nsx/vmw-nsx-network-virtualization-design-guide.pdf