My interpretation of the video
ARTPOP - An angel has been shot down by those who want to take advantage of a gift that they can't have. They always do that, that's how the industry and the humans work. When someone is better and has freedom, they have to shot them down to earth.
VENUS - It represents her depressions and how the little monsters never gave up on her. As she was nearly death, we keep on dancing to ARTPOP and believed in her, we cured her from her wounds and she rose back. We lead her to her comeback.
G.U.Y. - She's back. She shows herself powerful, she recovers. Then she trains (the golden dress scene with the bows) for the battle. The G.U.Y. project consist in use the DNA of the best men in earth to cleanse the industry and the humans, she doesn't have faith in them anymore, so she's going to replace them with clones of people like Jesus and Michael Jackson. She cames back to the industry HQ and takes over. The final dance scene shows her happy, the plan was a success, she has promoted worldwide kidness.
MANiCURE - A fun song meant to close the product and also help chart positions.