They support Geforce 600 and up. I don't even think Nvidia released a Geforce 800 except on mobile which is just a rebranded Geforce 700 so it's likely actually supported.
Note the 'M' at the end of the model number. The laptop GeForce models are different (and less powerful) than the desktop models. According to the website, the 840M supports "entry-level gaming", which isn't really the primary use case for Vulkan.
https://developer.nvidia.com/vulkan-driver
Why is this so, any idea?