That classes basically builds a microcontroller. It's Harvard Architecture with a split iROM and dRAM. Simple ALU, 16 bit CPU. You'd need one hell of a bread board to physically build it, though.
I'd definitely recommend TECS for folks looking to learn more about the many layers of abstraction sitting under their interpreter/VM. Also worth taking a look at the Little OS Book or the OSDev wiki for some more insight into a less idealized/more crufty architecture.
I wound up spending the most time playing around with chapter 9 (the Tetris part of Nand to Teris) and made a very basic ray-casting game a la Wolfenstein 3D: https://youtu.be/c-J7lwKWDN8
Basically it has you hands on work through the basics of every concept active in a modern computer save for networks and web.
You use software tools provided with the book to design memory, ALUs, intepreters, VMs, compilers Operating Systems and applications.
Available as a free online class at http://www.nand2tetris.org