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.
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.