Is there any GUI application that runs on both Mac OS X 10.0 Cheetah and macOS 10.13.4 High Sierra?
According to Wikipedia, Cheetah was shipped with AppleScript. So if you can have a Mac running Snow Leopard, according to comments of this question (and not the answer, it's strange), it seems that an AppleScript saved as app give a universal app (PowerPC G4 and above, or Intel). I haven't tested, but perhaps if you save this AppleScript:

display dialog "hello"


as app on the Snow Leopard's AppleScript Editor, it will run under Cheetah and High Sierra.

This AppleScript app is very simple, and display "hello" in a window, with a "OK" button. So this is a very simple GUI application.