The AppImage works on both PCs if the 'common' folder isn't present in the data folders location.
I don't know anything about Linux or AppImages, but I know that OXCE requires exactly one 'common' folder with the content that corresponds
exactly to that particular version of OXCE.
This should all be completely transparent to the player, even more so with AppImages, so please don't try to make any copies of the 'common' folder or move them from different installations or try to share them across different installations, or anything like that.
The best I can recommend is... delete ABSOLUTELY EVERYTHING and start fresh. Don't experiment.
As for the crashes... the most likely reason is that the content of the 'common' folder corresponds to an older version of OXCE (than the actual executable).
Even more specifically, I think it's because of missing entries in the `interfaces.rul`file, which I update quite often, basically with each release.