Miracast is for casting from a computer to a display such as a TV or projector. You can't cast from a computer to another computer so that's why there are no adapters like the one you mentioned.
@Secret-Squirrel See here for what I've been doing on my new computer. For some reason it's not supported on my old computer from 2012.
@hotaru.hino Can you link to said device? What's an HDMI capture device?
Is what I linked to Miracast? If so why can't I do it on my old computer? Are there any USB dongles/adapters out there that would allow this? If not how come?