Self-organized criticality (SOC) has attracted large interest as a key property for the optimization of information processing in biological neural systems. Inspired by this synergy, nanoscale self-organizing devices are demonstrated to emulate critical dynamics due to their complex nature, proving to be ideal candidates for the hardware implementation of brain-inspired unconventional computing paradigms. However, controlling the emerging critical dynamics and understanding its relationship with computing capabilities remains a challenge. Here, it is shown that memristive nanowire networks (NWNs) can be programmed in a critical state through appropriate electrical stimulation. Furthermore, multiterminal electrical characterization reveals that network areas can establish spatial interactions endowing local critical dynamics. The impact of such tunable and local dynamics versus the information processing in the network is experimentally analyzed through in materia implementation of nonlinear transformation (NLT) tasks, in the framework of reservoir computing. As for brain where cortical areas are specialized for a certain function, it is demonstrated that the computing performance of nanowire networks rely on the response of reduced subsets of outputs, which may show critical dynamics or not, depending on the specificity of the task. Such brain-like behavior can lead to neuromorphic systems based on self-organizing networks with reduced hardware complexity by exploiting their local and specialized behavior.