I won't pretend to know the internal workings of ACR, but display color management works the same as Photoshop and any other color managed application. The source color space - in this case linear ProPhoto - is converted/transformed into the display color space (display profile). It's a standard profile conversion (although the technical term is "transform", probably to emphasize that it's not user initiated, but automatically performed by the application, on the fly).
This is no different than 1.8 ProPhoto converted into a 2.2 display profile. One TRC (gamma) remapped into the other. Remember that the display has an inverse native TRC, so the net result is 1.
Opening from ACR into PS is technically an export, same procedure, straight color space conversion.