Context. According to the current understanding of star formation (SF), the regulation of this phenomenon in galaxy disks reflects a complex balance between processes that operate in molecular gas on local cloud scales as well as on global disk scales. Aims. We analyse the influence of the dynamical environment on the SF relations of the dense molecular gas in the starburst (SB) ring of the Seyfert 2 galaxy NGC 1068. Methods. We used ALMA to image the emission of the 1–0 transitions of HCN and HCO + , which trace dense molecular gas in the r  ∼ 1.3 kpc SB ring of NGC 1068, with a resolution of 56 pc. We also used ancillary data of CO(1–0) as well as CO(3–2) and its underlying continuum emission at the resolutions of ∼100 pc and ∼40 pc, respectively. These observations allow us to probe a wide range of molecular gas densities ( n H 2  ∼ 10 3 − 5 cm −3 ). The star-formation rate (SFR) in the SB ring of NGC 1068 is derived from Pa α line emission imaged by HST/NICMOS. We analyse how different formulations of SF relations change depending on the adopted aperture sizes and on the choice of molecular gas tracer. Results. The scatter in the Kennicutt–Schmidt relation, linking the SFR density (Σ SFR ) with the (dense) molecular gas surface density (Σ dense ), is about a factor of two to three lower for the HCN and HCO + lines compared to that derived from CO(1–0) for a common aperture. Correlations lose statistical significance below a critical spatial scale of ≈300−400 pc for all gas tracers. The SF efficiency of the dense molecular gas, defined as SFE dense  ≡ Σ SFR /Σ dense , shows a scattered distribution as a function of the HCN luminosity ( L ′(HCN)) around a mean value of ≃0.01 Myr −1 . An alternative prescription for SF relations, which includes the dependence of SFE dense on the combination of Σ dense and the velocity dispersion ( σ ), resolves the degeneracy associated with the SFE dense  −  L ′(HCN) plot. The SFE dense values show a positive trend with the boundedness of the gas, measured by the parameter b  ≡ Σ dense / σ 2 . We identify two branches in the SFE dense  −  b plot that correspond to two dynamical environments within the SB ring; they are defined by their proximity to the region where the spiral structure is connected to the stellar bar. This region corresponds to the crossing of two overlapping density wave resonances, where an increased rate of cloud-cloud collisions would favour an enhanced compression of molecular gas. Conclusions. These results suggest that galactic dynamics plays a major role in the efficiency of the conversion of gas into stars. Our work adds supporting evidence that density-threshold SF models, which argue that the SFE dense should be roughly constant, fail to account for spatially resolved SF relations of dense gas in the SB ring of NGC 1068.