Neither statement is true. First, we have entangled many systems other than photons. We have entangled trapped ions, neutral Rydberg atoms, superconducting qubits, nuclear spin states, and the list goes on. There are advantages and disadvantages to each quantum computing architecture.
One of the fundamental issues facing all quantum computing architectures is the question of scalability. It is not always clear how to go from 1 or 2 qubits to thousands or millions of qubits. Some architectures, such as trapped ions, lend themselves naturally to scaling. The significance of this work is that up to this point, it has been unclear how you might scale a photonic quantum computer. The authors of this paper have taken the first steps towards overcoming that obstacle.
As to your second statement, observed photon entanglement cannot be explained via classical optics. It has been shown to violate a Bell inequality, which is the hallmark of non-classicality in quantum mechanics.