The core of the issue lies in the timeline. The vSphere Client 6.0 was released in early 2015. Windows 10 reached general availability in July 2015.
This occurs with very old builds (before 6.0.0 Update 1). Download a newer build (e.g., 3562878 or 3634790). The installer checks OS version – newer builds recognize Windows 10.
Do not use vSphere Client 6.0. Instead:
If you get "Cannot connect to vCenter Server due to SSL/TLS error":
(formerly VMware Customer Connect) requires a registered account.
: Sites like VMware Arena maintain lists of direct download links for various versions, including Build 5112508 (Update 3). Installation & Compatibility