As for the random delay issue of multi-input multi-output (MIMO) nonlinear discrete-time multi-agent systems without dynamics models, an input gain compensation scheme is proposed. For the limited communication problem, we propose an event-triggered mechanism with a dead-zone operator. Firstly, we establish a compact form dynamic linearization data model on each work point of the agent using the pseudo partial derivative technique and propose the corresponding parameter estimation approach. Based on the obtained data model, by combining with the symbolic graph theory and researching the cooperative-competitive relationships among agents, we propose an event-triggered data-driven bipartite formation control algorithm. Finally, we prove the convergence of the designed algorithm using the Lyapunov stability theory, matrix theory, and contracting mapping principle and further demonstrate the effectiveness and correctness of the developed algorithm through simulation studies and hardware tests.