Aims: We study the feedback of star formation and nuclear activity on the chemistry of molecular gas in NGC 1068, a nearby (D = 14 Mpc) Seyfert 2 barred galaxy, by analyzing whether the abundances of key molecular species such as ethynyl (C2H), which is a classical tracer of photon dominated regions (PDR), change in the different environments of the disk of the galaxy. Methods: We used the Atacama Large Millimeter Array (ALMA) to map the emission of the hyperfine multiplet of C2H(N = 1-0) and its underlying continuum emission in the central r ≃ 35″ (2.5 kpc) region of the disk of NGC 1068 with a spatial resolution 1.̋0 × 0.̋7 (≃ 50-70 pc). We used maps of the dust continuum emission obtained at 349 GHz by ALMA to derive the H2 gas column densities and combined these with the C2H map at matched spatial resolution to estimate the fractional abundance of this species. We developed a set of time-dependent chemical models, which include shocks, gas-phase PDRs, and gas-grain chemical models to determine the origin of the C2H gas. Results: A sizeable fraction of the total C2H line emission is detected from the r ≃ 1.3 kpc starburst (SB) ring, which is a region that concentrates the bulk of the recent massive star formation in the disk traced by the Paα emission complexes imaged by the Hubble Space Telescope (HST). However, the brightest C2H emission originates from a r ≃ 200 pc off-centered circumnuclear disk (CND), where evidence of a molecular outflow has been previously found in other molecular tracers imaged by ALMA. We also detect significant emission that connects the CND with the outer disk in a region that probes the interface between the molecular disk and ionized gas outflow out to r ≃ 400 pc. We derived the fractional abundances of C2H (X(C2H)) assuming local thermodynamic equilibrium (LTE) conditions and a set of excitation temperatures (Tex) constrained by the previous multiline CO studies of the galaxy. Our estimates range from X(C2H) ≃ a few 10-8 in the SB ring up to X(C2H) ≃ a few 10-7 in the outflow region. The PDR models that incorporate gas-grain chemistry are able to account for X(C2H) in the SB ring for moderately dense (n(H2) ≥ 104 cm-3) and moderately UV-irradiated gas (UV-field ≤ 10 × Draine field, where 1 Draine field ≡ 2.74 × 10-3 erg s-1 cm-2) in a steady-state regime, which depending on the initial and physical conditions of the gas may be achieved by 105 yr or as late as 107 yr. However, the high fractional abundances estimated for C2H in the outflow region can only be reached at very early times (T ≤ 102-3 yr) in models of UV or X-ray irradiated dense gas (n(H2) ≥ 104-5 cm-3). Conclusions: We find that the transient conditions required to fit the high values of X(C2H) in the outflow are likely due to UV or X-ray irradiated non-dissociative shocks associated with the highly turbulent interface between the outflow and molecular gas in NGC 1068. Although the inferred local timescales are short, the erosion of molecular clouds by the active galactic nucleus (AGN) wind and/or the jet likely resupplies the interface working surface continuously, making a nearly steady state persist in the disk of the galaxy.