The Web Client by itself works without NPAPI. The issue is with the Client Integration Plugin, which provided some additional functionality. Some of this functionality has been moved into the standalone VMware Remote Console application (VMRC). You can see more specifics in this KB article:
Downloading and Installing the standalone VMware Remote Console (VMRC) in vSphere 5.x and 6.0 (2091284):
We are also working on the rest of the functionality in various ways.
