I think I've arrived at a provisional definition of Solo RPGs, along the lines of the Lumpley Principle (see definition of LP at http://big-model.info/wiki/Lumpley_Principle):
System (including but not limited to 'the rules') is defined as the means by which a person commits to (settles on) imagined events during play.
The underlined part is my modification. I'm not sure yet if the best word is "commit" or "settle", so I leave both for now.
Does it matter? Who knows. I'm hoping it tells me or someone something about solo RPGs that takes their design somewhere interesting. Definitely puts the emphasis on how a player settles on what action "really happened" in play. You know, the stuff you report in your actual plays or that makes it into your write ups (if you write).
See some ongoing discussions here: