Partially true, internally libraries represent the rotor as just four scalars and can convert these to a quaternion. However, to actually make use of the rotor to do anything useful, e.g. interpolate, which is a power quaternion math has innately, you need to provide a lot more external information; plane origin vector, bivector, angle. A 3D file format storing the transformations between joints of the skeleton of a character for example would have to provide these extra bits of information in order to store the frames to perform inverse kinematics.
Likewise, if you needed to store or transmit spherical camera interpolations or non-player or player character transitions over a network this information would also have to be provided. You could perhaps do some optimization, e.g. only sometimes transmitting the origin once and then only sending the bivectors and angles in some cases which still would waste bytes and increase complexity. And, sometimes you couldn't so you'd have to send the whole thing.
But, with a quaternion you get this for free without any logical gymnastics via the previous four scalars to the next four scalars between delta frames. And, in the case of slerp only the lambda of time.
Now you can argue that a rotor could be used locally and then when storage/transmission is required you could convert to and use quaternion math to perform the necessary interpolations and thereby get the space savings. However, this article is specifically asking for the complete removal of quaternions from the field of computer science.
Unless I'm misunderstanding. Though I haven't seen a code example where rotors don't require this extra information. For example, in libvsr they have examples that require all these pieces for each frame. However, maybe that is an inefficient or naive implementation.
I did find this: http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/01...
Which provided a formula for rotor slerp:
R(lambda) = (1.0 / sin(theta)) * (sin((1 - lambda) * theta) * R0 + sin(lambda * theta) * R1)
If that is the case, then the bare minimum information required is still more than a quaternion. We'd require the lambda, theta, and R0 (4 scalars), R1 (4 scalars).