May be the explanation is wrong.

Anyway, Machu Picchu gives food bonus only two cities or one cities, sometimes does not give anywhere at all

never all cities.

How does it work actually?

Yeah, I don't get it either. Machu's city:

food gains: 598 (Stonhenge+Angkor),

food output: 35.

Result: some of my cities get 14 food.

I expected 299 food/city, which would be insanely op. If it was 17 food/city, I'd understand.

I'm seeing the bonus food entry  on outposts and cities founded *after* Machu Picchu was built. So, intentionally or not, it's only giving the bonus to *new* construction. Also, its showing on outposts when the tooltip suggests it'd only be for cities. I'm guessing the actual food amount it gives is the amount produced in the district it's in rather than the whole city, but I haven't been able to test that yet.