Reg Edwards wrote:
It is used to reduce the common mode current which sometimes flows in
coaxial and balanced-pair lines.

It is not a transformer. The 1-to-1 is meaningless. It is just a pair
of wires wound together, as one wire, on a ferrite core. Or in your
case a number of ferrite slugs or rings are placed over a coax line.

In brief, it is just a choke.

But a choke with two wires wound through it is two inductors that also
have mutual inductance between them, and if that doesn't define a
transformer, what does?

It is true that this device acts as a choke for common mode current
(the component of the two currents through the two conductors that is
in phase). A choke is an inductance, which produces voltage across
the terminals of the conductor passing through that is proportional to
the rate of change of the current. In this case, it produces a
voltage across both the shield section inside the cores and also
across the center conductor inside the cores, that is proportional to
the rate of change of the common mode current. It is this voltage
that alters the displacement currents in the two terminals at the
antenna end, to make them look like a more balanced signal, and at the
transmission line end, more like a single ended one.