The weird thing was the obsession with robotic animals that's not in the movie at all. I think it was meant to underline the apocalyptic world where living things have mostly disappeared.
The best thing for me about blade runner is the visual style of the movie. It spawned an entire visual genre of cyberpunk and most cyberpunk franchises still lean very heavy on this. The darkness with neon, the 80s vision of the computer, the heavy branding and Eastern influences, the music etc.
It's still my favourite genre for techno party cosplay.