As save-games and configs of my GOG Linux games are normally(!) outside of the installation folders (found them in my home-folder, under .local or .config), I simply install such new version .sh file into the same locations (overwriting the existing installation). But I do not know for sure, if this is the best solution in all cases.
Anyway you can easily try it by yourself after backing up your game-folder (simply zip it). This way you will not lose anything if overwriting game files will mess something up.
EDIT: maybe it is worth finding the save-game/config folder and back it up, too. Just in case the new version messes with config files.
Your question reminded my immediately about one of my favorite 35c3 talks Butterbrotdosen-Smartphone - Mein DIY-Smartphone-Bau from 2018-12-29. It is in German language, but has an English translation, too. Maybe it can give you some good starting ideas?
Story, Translated with DeepL.com (free version)> I would like to show you how I built a smartphone from a Raspberry PI. The problems and difficulties I encountered and the solutions I found. The project is not yet finished, there are still a few small things missing. Nevertheless, I want to show you my smartphone in the practical sandwich box and tell you how it came about. > > I had no idea that building a smartphone could be so complicated. Raspberry Pi + touch display is not all there is to think about in this project. At the moment, the smartphone project lives in a sandwich box and attracts attention on the subway. If the power bank can passthrough, that’s an advantage, I’ve found. Setting up the X and Y axes on the touch display so that you can also use the on-screen keyboard was not so easy. And I had to realize that Landscape is not the right size to work smoothly. Most Linux programs are not directly touch-compatible or require too much memory. Then there were also big challenges! Learning to solder was one of them. First learning how to solder, then learning how to desolder, and then daring to use the PI. I would like to tell you these and other stories about building my smartphone.
Auf den von mir besuchten drei Demos wurde für Demokratie, Menschenwürde und Vielfalt demonstriert. Und natürlich gegen Rechtsextremismus und Hass.
Diese Demos waren explizit nicht gegen demokratische Parteien gerichtet und das war auch gut so! So standen und marschierten wir (sehr viele Menschen, von jung bis alt, von links bis rechts) vereint gegen das Nazi-Pack.
Ich hörte zufällig einen CSU Politiker sinngemäß sagen (beim Vorbeiziehen dem Lokalreporter antwortend), dass er es gut und wichtig findet, hier zusammen mit u.a. den Kollegen von Grünen und SPD Gesicht zu zeigen.