Take a look at 0.101001000100001... This number is also non-repeating, but obviously doesn't contain all numbers with finite digits.
The property you're looking for is called to be a normal number. Pi is assumed to be one, but it hasn't yet been proven.
However, in a sense this is an unremarkable property as almost all real numbers are normal. :)
I considered just installing the new .sh file in the same location, but wasn't sure whether that breaks my saves in the worst case. So it's reassuring to hear that others had success with this method. I'll try it when I get an update for one of my Linux native games. Thank you :)