Proportional electroluminescence (EL) in noble gases is used in two-phase detectors for dark matter search to record (in the gas phase) the ionization signal induced by particle scattering in the liquid phase. The "standard" EL mechanism is considered to be due to noble gas excimer emission in the vacuum ultraviolet (VUV). In addition to it, there are two alternative mechanisms, producing light in the visible and near infrared (NIR) range. The first is due to bremsstrahlung of electrons scattered on neutral atoms (so-called neutral bremsstrahlung, NBrS). The second, responsible for electron avalanche scintillations in the NIR at higher electric fields, is due to transitions between excited atomic states. In this work, we have for the first time demonstrated two alternative techniques of the optical readout of two-phase argon detectors, in the visible and NIR range, using a SiPM matrix and electroluminescence due to either neutral bremsstrahlung or avalanche scintillations effects. The amplitude yield and position resolution were measured for these readout techniques, which allowed to assess the detection threshold for electron and nuclear recoils in two-phase argon detectors for dark matter search. It should be emphasized that this is the first practical application of the NBrS effect in detection science.