Cooperativity is a hallmark of spontaneous biopolymer folding. The presence of intermolecular interactions could create off-pathway misfolding structures and suppress folding cooperativity. This raises the hypothesis that thermodynamic competitivity between off-pathway misfolding and on-pathway folding may intervene with cooperativity and govern biopolymer folding dynamics under conditions permitting large-scale intermolecular interactions. Here we report direct imaging and theoretical modeling of thermodynamic competitivity between biopolymer folding and misfolding under such conditions, using a two-dimensional array of proton-fueled DNA molecular motors packed at the maximal density as a model system. Time-resolved liquid-phase atomic force microscopy with enhanced phase contrast revealed that the misfolding and folding intermediates transiently self-organize into spatiotemporal patterns on the nanoscale in thermodynamic states far away from equilibrium as a result of thermodynamic competitivity. Computer simulations using a novel cellular-automaton network model provide quantitative insights into how large-scale intermolecular interactions correlate the structural dynamics of individual biomolecules together at the systems level.