I wrote it in my native language which is Polish and it's not translated so I doubt it'll be of any use to you regretfully :(
Even if the paper is in Polish, I would still love to read it (with the help of Google Translate) and look at the pictures if there are any. If I were new to the subject I would probably be doomed at reading it, but since I have a background in 2D virtual reality, I can probably benefit from it even if I misinterpret some of the text. Also, I haven't checked on the academic portals yet, but I wouldn't be surprised if your paper was still the only one about 2D virtual reality in 2020.
That being said, if it's a hassle to send (with or without a paid link) then you shouldn't go out of your way if you don't have much time. (The same goes for replies here since we're all busy.)
Re: parallax
Your description of parallax makes sense to me (especially for the cylinder version). I should definitely think about it further, because it would be a shame to miss a cool feature over my own ignorance. Additionally, you can definitely do parallax for games that exist in an xy-plane but are rendered in virtual reality.
The analogy I would use is a large semi-transparent square cloth representing the world map and a smaller spherical light bulb that represents what the player can see at any given moment. The light bulb projects a subset of the world map on the walls. This system works relatively well without much stretching of the cloth for a <=180 degree field-of-view. In this system you could basically do parallax the same as traditional 2D games (with different layers moving at different speeds in the xy-plane).
And nausea is ironically a huge issue in 2D virtual reality in my experience (it was counter-intuitive to me at least). I don't think it's an inherent problem, it's just hard to design 2D virtual reality games (at least for now).