Why do the Duga-1 dipoles look like an array of birdcages?
This is a cage dipole antenna (or an array of cage dipoles to be exact). It works just like a dipole, but has a wider bandwidth. The thicker the dipole, the wider the bandwidth.

RF does not care if the conductors are hollow cylinders, solid surfaces, cages or mesh as long as size of the "holes" is signifficantly smaller than the wavelength (that is also why you can look into the microwave oven through tiny holes and not get cooked in the process).

Examples:


https://en.wikipedia.org/wiki/Dipole_antenna#Other_variants
https://en.wikipedia.org/wiki/Ukrainian_T-shaped_Radio_telescope,_second_modification