Condensed matter physicists have shown using quantum information that in many condensed matter systems, entanglement entropy only scales as the area of the boundary, and not the volume. This is the basis for the density matrix renormalization group and Projected Entangled Pair States (PEPS). Does this also explain the holographic principle in quantum gravity?
Nope, the very fact that the entanglement entropy is - naturally - proportional to the surface area does not explain the holographic principle because the holographic principle, reduced to the corresponding entropy bound, implies that the total entropy of one of the systems can't exceed $A/4G$ where $A$ is the surface. The entanglement entropy is just one tiny term of the entropy, a degree of correlation between two subsystems, so its being proportional to the area is a much weaker and less surprising statement than the holographic principle.
Quite generally, non-gravitational physical systems are simply not holographic in the space (bulk) that they occupy. Only (quantum) gravitational systems obey the holographic principle. In the context of AdS/CFT or AdS/anything, the holographic principle is encoded in the description of the CFT or anything by its having a secret extra (fifth) dimension of spacetime.