The fact that there are 3 of them, all identical when they step out of the machine, disproves that they are unique. Unique means that there is only one, and now there are three.
The point is not that they are unique or not. The point is they are three seperate people who happen to have the same physical characteristics and memories as each other, but they each have their own consciouness, POV, and occupy different points in space (so I guess they're unique anyway). Are you claiming that the three people who step out of the transporter are one person?
The whole problem is, if personal identity can survive teleportation, and a teleportation results in three copies being made (each of which qualifies as a person), which copy is me?