The voight-kampff test measures empathetic responses. The questions asked are designed to elicit an emotional response. Most of the questions, in some manner, involve animals.
Why does that elicit an emotional reaction?
Because in Blade Runner, all of the animals are dead.

The film never outright tells you "Humanity fucked up the planet so much with pollution and wars that the sun is all but blocked out by the waste, and now the only living creatures left are humans and replicants, and humans deal with that existential horror." It lets it linger.

Every animal you see in Blade Runner is an artificial, synthetic being. Owning them is a status symbol. Hucksters sell knock-off animals at market stalls. The wealthy own top-of-the-line versions.
That's how humanity deals with its grief.

The very best thing about Blade Runner is that it never tells you any of this outright.
Because the characters in the film are too traumatised to speak it directly.
They remember what living in a world with real animals was like.

We all know that characters in the film represent certain animals. Rachel talks about a spider she remembers, Tyrell lives with an owl, Roy howls like a wolf, Deckard dreams of a unicorn. It can be a fun game to match the character to the animal they represent.

But then you realiize that all of the characters are carrying the trauma of the destruction of the planet's ecosystem with them, and have internalised their own horror at that.
Then you understand why they're all just animals. In a world without them, someone has to be.

The real question that Blade Runner asks is this;
Can we be more than we have been?
I think that's probably my favourite point of the film. Some characters were designed to be who they are; others became who they are by trauma, grief, or hopelessness.