You may have been confused by my suggestion to back up your installation (save it somewhere local to you, on a thumbdrive or the like).
I looked at the log and it doesn't say anymore than what you reported:
07:26:30.9 9/1/2024: GameEx: Version 5.31: Starting Log
07:26:30.9 9/1/2024: Operating System Platform: Win32NT
07:26:30.9 9/1/2024: Operating System Name: Windows XP
07:26:30.9 9/1/2024: Operating System Version: 5.1.2600
07:26:30.9 9/1/2024: ERROR: An error occured while checking for previous instance of GameEx
07:26:30.9 9/1/2024: This can be caused by a bad windows or .net framework install.
07:26:30.9 9/1/2024: GameEx will likely function incorrectly as it cannot check for running processes
07:26:30.9 9/1/2024: GameEx will now exit with errors
07:26:30.9 9/1/2024: Application-defined or object-defined error.
07:26:31.0 9/1/2024: ERRORS DETECTED: EXITING
You could try to install the latest version, but be prepared for the possibility of having to update configurations, update emulators, etc. due to compatibility. Over-the-top install would not be recommended for such a jump in versions as the gameex.ini format is much different.
Also, I am not sure that you will not run into issues due to monitor, controllers, or other peripherals in your cab as you are looking at 11+ year old kit. You may also run into .NET errors due to backwards compatibility. .Net 4 is the oldest that is currently supported in the latest versions of GameEx, but that will not last for much longer per Tom's post HERE.
If the original manufacturer is still around, you may be able to get some details about your specific system and upwards compatibility for OS with the PC and peripherals for a newer OS, although hard for me to say if possible not knowing what was installed in your kit.