The reason why the Standard Model of particle physics does not include a specific box for the graviton is because the Standard Model itself does not incorporate gravity. The Standard Model describes the electromagnetic, weak, and strong nuclear forces, and it accounts for the elementary particles associated with those forces, such as photons, W and Z bosons, and quarks.
Gravity, on the other hand, is described by the theory of general relativity, which was formulated by Albert Einstein. In the framework of general relativity, gravity is not mediated by particles like the other fundamental forces. Instead, it arises due to the curvature of spacetime caused by the presence of mass and energy.
The graviton is a hypothetical particle that is proposed within the framework of quantum field theory as the mediator of the gravitational force. However, the graviton has not been experimentally observed or included in the Standard Model because the unification of gravity with quantum mechanics is still an open problem in theoretical physics. The current understanding is that a consistent quantum theory of gravity would require a deeper understanding of the fundamental nature of spacetime and the quantization of gravity.
So, to summarize, the absence of the graviton in the Standard Model is not due to its identification as a virtual particle, but rather because the Standard Model does not encompass gravity in its current formulation.