I still don't understand why the unicorn is a symbol of his being a replicant. It makes more sense to me that the unicorn is a symbol for Rachel and/or the miracle of humanity and life.
Ridley Scott colorfully described the importance of the origami unicorn in the aforementioned IGN interview that I linked. When Harrison Ford expressed that Deckard shouldn't be a replicant during the making of the original film, Scott responded, ”But you have to be, because Gaff, who leaves a trail of origami everywhere, will leave you a little piece of origami at the end of the movie to say, ‘I've been here, I left her alive, and I can't resist letting you know what's in your most private thoughts when you get drunk is a f***ing unicorn!'" A popular notion of the replicant theory has speculated that Gaff's role in the narrative has him operating as a 'handler' to Deckard, possibly observing his detective work and psychological development as an experimental or upgraded version of the Nexus android. By preserving the daydream sequence in both the 'director's cut' and '
Final Cut, it provides pivotal context to the origami as an outright reveal to Deckard and the audience that he knows exactly what's inside his thoughts, much like how Deckard easily uncovered Rachel's memories as part of his investigation. Thus, his nod after picking the figure off the floor and recollection of Gaff's final remark about morality serves as a recognition of his own existence as a replicant. Also, J.F. Sebastian clarifies in his conversation between Pris and Roy that he does "genetic design work for the Tyrell Corporation. There's some of me in you." While the film hammers on the shared similarity being their accelerated aging, his involvement with hereditary development means that he could possibly dictate what subject matter becomes the memory basis for every replicant to make them feel more human. If each android did, indeed, have "some [part] of me in you," Sebastian likely took inspiration from various interests and/or items inside his own apartment, particularly the unicorn figurine (pictured below in the upper right-hand corner) being evidence for Deckard's case.