This paper presents a unified derivation of electromagnetic and gravitational structures within the Meaning-Based Constraint (MBC) framework. Unlike standard gauge theories that postulate gauge symmetry, this work demonstrates that electromagnetic dynamics emerge inevitably from the maintenance of the Four-Point Interference Invariant (I4). We show that finite closure residuals generate phase gradients, which necessitate compensating transport fields identified as electromagnetic fields. Furthermore, we extend this framework to demonstrate the quantization of charge, the emergence of stable particle-like structures (closure vortices), and the generation of non-Abelian gauge structures and mass hierarchies. Gravity and electromagnetism are identified as scalar and rotational manifestations of a common closure-residual structure, providing a unified foundation for fundamental physical interactions without independent electromagnetic postulates.