@ywp
As the documentation you shared says, Export is not supported in a browser, so yes, you can only use this feature from a Mobile device.
Re: That Limitation says it only applies to Export (no mention of Import limitations).
That's true but the Import needs a file to reference, otherwise it errors out. Because you cannot Export the correct file type to a Windows machine, Import shows the error.
As for that Windows PowerApp App, it has been plagued with issues from the start so I avoid it now. A few years ago MS said that you could test Load/Save Data inside of this app but I could never get it to work for me, so just gave up. I suspect it's the same for what you are trying to do with Export/Import.