If it means rotors can be used to give a simple formula for rotations in 3D space, then it also applies to quaternions.
If it means the space of rotors is three-dimensional, then it's false: rotors have 4 coordinates, a + b x^y + c y^z + d x^z, just like quaternions.
Does it mean something else? Something that applies only to rotors and not to quaternions?
It's also easy (after reading the article) to understand the operations that can be performed on these things.
It's not as obvious what i, j and k in the quaternions correspond to, or why they have the multiplication table that they do. It's an algebraic construction, not a geometric one and hence more difficult to visualise.
Quaternions and rotors are exactly the same in practice, but the intuitions are very different. The intuition behind rotors involves planes and lines in 3D, whereas the intuition behind quaternions typically involves a unit hypersphere; there's a 3B1B video on quaternions where you can learn more about them.
Note that even if you do restrict q to have unit norm, q and -q still denote the same rotation! (In other words, the space of rotations isn't really S^3, but projective space RP^3.)
I'll be sure to check out the 3B1B video, I keep seeing them recommended and I think they might a good resource to recommend to my students.