Can nonpolar molecules exhibit dipole-dipole forces?
Short answer: there are many electrostatic interactions between two non-polar molecules.

Beyond monopole (full charges) and permanent dipole moments (polar molecules), there is a full multipole expansion for the electrostatic potential around any molecule. (This is technically true for atoms and ions too, but higher-order terms are really only useful for molecules.)

So there are electrostatic potential energy interaction terms for charge-dipole, dipole-dipole, dipole-quadrupole, quadrupole-quadrupole, etc.

These terms are important - the quadrupole-quadrupole interactions dictate the orientation of the benzene dimer and $\ce{CO2}$ dimer in your example.1

The problem is that most of these interactions die off very quickly. The quadrupole-quadrupole term is:1

$$E(r)=\frac{-\Theta_1\Theta_2}{4\pi\epsilon_0r^5}\times\Gamma(\theta_1,\theta_2,\phi)$$

So roughly $1/r^5$, compared to $1/r^3$ for dipole-dipole interactions, or $1/r^6$ for dispersion forces like induced-dipoles.

When such molecules are close, the quadrupole moments (and other multipole electrostatic terms) can dictate packing and distances, but are not as strong or as long-range as dipole-dipole or charge interactions.