The S=2 anisotropic triangular lattice alpha-NaMnO2 is studied by neutron inelastic scattering. Antiferromagnetic order occurs at T ~ 45 K with opening of a spin gap. The spectral weight of the magnetic dynamics above the gap (Delta ~ 7.5 meV) has been analysed by the single-mode approximation. Excellent agreement with the experiment is achieved when a dominant exchange interaction (|J|/k_B ~ 73 K), along the monoclinic b-axis and a sizeable easy-axis magnetic anisotropy (|D|/k_B ~ 3 K) are considered. Despite earlier suggestions for two-dimensional spin interactions, the dynamics illustrate strongly coupled antiferromagnetic S=2 chains and cancellation of the interchain exchange due to the lattice topology. alpha-NaMnO2 therefore represents a model system where the geometric frustration is resolved through the lowering of the dimensionality of the spin interactions.