Lumia 950 supposedly can utilize continuum using HDMI cable adapter.
Does this cable also work with Lumia 640 for the same purpose?
Lumia 640 does not support the minimum requirements for Continuum. The processor of Lumia 640 is an old chipshet. It does not require a phone that came preinstalled with the Windows 10 Mobile as said by @kelvinelove. Continuum was even demonstrated in a low end phone by a hacker. I don't have that link now. However the performance was terible. There is a reason that there are Minimum requirements.
Here is the minimum requirements for Continuumn:
Yes, they will be in future. At the price point of L640 you can get all the minimun requirements. Microsoft may have skipped it on L640 as both W10M and continuum was at infancy during the phones release.
I'm gonna have to say "no", because, first off, the Lumia 640XL does not support Continuum.
Continuum is available on Windows 10 Mobile specific hardware, that is, phones that were designed specifically to work with Windows 10 Mobile as their initial OS. The Lumia 640XL supports Windows 10 Mobile, and can get it through an upgrade, but it doesn’t have the hardware to take advantage