There are lots of brick presses available on Alibaba, starting at about $900. Some of them look very much like this one. Cheap ones are available from India and Zaire. China mostly uses larger, higher-volume machines. Also, most people put a little cement in earthen bricks, about 5%. They hold together better. It's common to put in holes for rebar, which is pretty much mandatory in earthquake country.

If you want to build from earth, there's rammed earth construction. It's even simpler than compressing earth into bricks. You set up wood forms, as if pouring concrete, put in about 4" of dirt, and pound it into sandstone. This can be done by hand, or with an air hammer.

All this works if the soil composition is reasonably suitable. There are simple tests. (Too much clay is bad.) It's usually possible to find nearby sources for suitable dirt.

This guy seems to be re-inventing the wheel.

The whole point is to reinvent the wheel. Which I think speaks to the practicality of this whole endeavor.