We investigate the collective gyrotropic modes in a linear chain of ferromagnetic nanodots in a skyrmion magnetization state. Individual skyrmions in the dots (with thickness about of 1 nm and radius about of 100 nm) are assumed to be stabilized by interplay of isotropic exchange and Dzyaloshinskii-Moriya exchange interactions, magnetic anisotropy and magnetostatic interactions. Weconsider the dipolar and quadrupolar interactions between moving skyrmions in the dots as prevailing mechanism responsible for dynamic interdot magnetostatic coupling. The frequency dispersion relations of the collective skyrmion gyrotropic excitations are calculated for Bloch and Neel skyrmion configurations and related differences in the frequencies are discussed. The accounting of magnetostatic interactions between the skyrmions removes phase degeneracy of the gyrotropic frequency existing for isolated skyrmions and allows distinguishing the Bloch and Neel skyrmionic configurations by their dynamic response. The interdot magnetostatic coupling and frequency bandwidth are maximal for the large-radius Bloch skyrmions in the relatively thick dots.