To me it seems that in the future they for some reason need to access files that can only be opened on that computer.
If time travel is indeed possible and relatively common, it might be a better business decision to just send someone back in time to fetch a working version of that computer than try to recreate one from archived documentation (if any of it survived).
If there is something special about that computer it can surely just be executed in an emulator running on any future computer that is more powerful and uses less power, like a Raspberry Pi or its future equivalent.
This would still require having the original documentation on how the computer operated. Not to mention, some software (notably some retro console games) rely on quirks or flaws in the silicon itself, and don't actually run on a "perfect" emulator.
If time travel is common and either of these issues is raised then sending someone back to bring the real computer might be the easiest option.