Polyatomic gas cloud expansion into vacuum under pulsed laser ablation is studied on the basis of one-dimensional model kinetic equation. To account for the influence of internal energy on the vapor-gas cloud parameters (density, temperature, and velocity) a model kinetic equation of the BGK-type is applied, which considers the energy exchange using a two-temperature model. In this approach, the collision integral is approximated by the sum of two terms corresponding to elastic (translational relaxation) and inelastic (rotational relaxation) collisions. Note that the vibrational energy is not taken into account in this paper. The independence of the differential part of transfer equation from the rotational energy makes it possible to reduce the equation to a system with two functions. A comparison of the gas flow macroparameters obtained by the kinetic equations and the DSMC is carried out. The influence of the number of rotational degrees of freedom on the evolution of average temperature and on the gas parameters is shown. The calculations are performed on non-uniform grids in the phase space with global dynamic velocity mesh adaptation to suppress the "ray effect".