TLDR: Use the engine to make a game however you want, I don't care. It can be free or commerical, either is fine. All that you need to do is open source any changes that you make to the engine, as outlined in the LICENSE in the file.
This engine is far from finished to the point that I don't even know if you can actually make a game using it yet. It's in like the pre-pre-pre-pre-pre alpha stage or something.
I wanted to open-source this now as there is zero advantage for both myself or Madnight Games to keep this closed source. Pull requests with fixes and improvements are more than welcome!
This engine is just a library that links into your game code, so you'll create a new git repository with the engine (and its nugget submodule) added as a submodule, then scaffold your game code on top of it.
For the full walkthrough — toolchain setup, adding the submodule, scaffolding your game, building, and running it in an emulator — see getting-started/README.md.
If you wish to dynamically load assets rather than having them hardcoded as header files or whatever then you will need to take a look at pcsx-redux's authoring tool.
In the cdrom directory you will see an example toc.json that you can pass into the authoring tool to generate your ISO.
Huge thank you to the following for their involvement in getting this engine started and understanding so much about psyqo; along with the PS1 and its hardware.