Searches for dijet resonances with sub-TeV masses using the ATLAS detector at the Large Hadron Collider can be statistically limited by the bandwidth available to inclusive single-jet triggers, whose data-collection rates at low transverse momentum are much lower than the rate from standard model multijet production. This Letter describes a new search for dijet resonances where this limitation is overcome by recording only the event information calculated by the jet trigger algorithms, thereby allowing much higher event rates with reduced storage needs. The search targets low-mass dijet resonances in the range 450-1800 GeV. The analyzed data set has an integrated luminosity of up to 29.3 fb^{-1} and was recorded at a center-of-mass energy of 13 TeV. No excesses are found; limits are set on Gaussian-shaped contributions to the dijet mass distribution from new particles and on a model of dark-matter particles with axial-vector couplings to quarks.