Quotation from the Wikipedia article about vacuum energy:
"The theory considers vacuum to implicitly have the same properties as a particle, such as spin or polarization in the case of light, energy, and so on."
In quantum field theory, why is vacuum considered to have the same properties as a particle?
In nonrelativistic (particle-based) QM, many properties of particles cannot be explained. There is no reason that electrons are spin 1/2, or they must have antisymmetric wavefunctions while photons have symmetric ones, or even why particles of the same kind are indistinguishable. These are all put into the theory by hand. We add a "spin" coordinate to the wavefunction for every particle and impose symmetry constraints on multi-particle wavefunctions because these modifications give the right physics. But the changes have no mathematical backing (they are axioms, or more accurately "inputs to the model"), so we can't answer "why."
In QFT, a lot of these questions are answered. Each type of particle corresponds to a single field on spacetime. Every individual particle is a (quantum of) excitation on the corresponding field. (This explains why particles come in only a few "kinds", and are indistinguishable within their kind.) The apparent properties of particles derive from the properties of the field. Photons are spin 1 and bosons because their underlying field is a vector field, and electrons are spin 1/2 and fermions because their underlying field is a Dirac spinor field. It simplifies the problem that QM poses, of "why do the nonillions of fundamental particles I see every day come in only a few types?" down to just "why do these few fields have the types (scalar/spinor/vector/etc.) they have and the couplings they have?". (Of course, this residual question seems nigh-unanswerable.)
Once you move from particles to fields, the vacuum becomes more interesting. Every point of spacetime contains every field (this is just as true classically as it is in QFT). This is true also of "empty" spacetime, containing no particles. Such a vacuum will still have all the fields in them; they will just not be excited. So a statement like "electrons have spin 1/2" applies to all spacetime, including the vacuum, since the electron field is "attached" to all spacetime, including spacetime with no actual electrons.
The phrasing you find on Wikipedia is a bit misleading, IMO. The vacuum of course contains zero spin angular momentum, zero charge, etc. And the properties of the fields (their spins, their charges, etc.) hold in all spacetime, including non-empty spacetime.
In quantum mechanics, and physics in general, the math gives an accurate description of nature. People also explain with words what is going on and why the math applies. The concepts are often very different from everyday life and confusing. People simplify, and the explanations are often a compromise between accurate and understandable.
The wave-particle duality is a good example of this. A photon or electron is often described as a wave or a particle. They aren't really either one. They are something like both a classical wave and a classical particle, but also different. See How can a red light photon be different from a blue light photon?
QFT is based on the idea that space is filled with fields. Particles are excitations of the field.
In QFT, a vacuum isn't an empty region of space. For space to be empty, the fields would have to be $0$. In reality, they are continually fluctuating. This means the vacuum is full of virtual particles.
Virtual particles are another example of a compromise, but they too have particle-like and wave-like properties.
The reason? As always in real physics, it's because it works, capturing real phenomena. Perhaps the clearest demonstration of this is the phenomenon of squeezed vacuum.
