It starts with simply accepting that dark energy is part of the unremovable background of spacetime (in particular, his paper considers a de Sitter vacuum with a straightforward positive cosmological constant, and treats it as fully described by classical General Relativity (GR)) and then proposes an emergent thermal-entropic force that may produce deviations from General Relativity on galactic and cluster scales by way of a long-distance entanglement among the fundamental material from which this take on perturbative gravity emerges.
That fundamental material -- strings (sec 2.3) -- generating the thermal-entropic force does not feel electromagnetism, and so is dark. That fundamental material additionally is a component of the matter tensor in the low-temperature General Relativistic limit of his theory (eqn 4.23).
Verlinde's theory is, in fact, a "cold" "dark" "matter" one; as the cosmological constant is involved too, it unsurprisingly reproduces the successess of \Lambda-CDM. (CDM == cold dark matter). The only qualification of this is that "matter" is the standard GR definition of everything that is not the gravitational field content. It's not much like the matter of the Standard Model (SM), while WIMPs are expected to be by virtue of some extension of the SM. (MACHOs, by contrast, can have very little to do with SM or extended-SM particles.)
Nevertheless, the major difference between Verlinde's theory and the standard cosmology is the emergence of the standard cosmology from string theory.
Quoting the paper: "in our ... framework one has to add a dark component to the stress energy tensor, which behaves very much like the cold dark matter needed to explain structure formation, but which in its true origin is an intrinsic property of spacetime rather than being caused by some unknown particle".
In other words, the paper proposes that some (sec 8.2) of the dark matter of the standard cosmology can emerge from strings in a way that does not produce a particle like a heavy neutrino.
(The paper is interesting many other ways, though.)