On-demand modification of the electronic band structures of high-mobility two-dimensional (2D) materials is of great interest for various applications that require rapid tuning of electrical and optical responses of solid-state devices. Although electrically tunable superlattice (SL) potentials have been proposed for band structure engineering of the Dirac electrons in graphene, the ultimate goal of engineering emergent quasiparticle excitations that can hybridize with light has not been achieved. We show that an extreme modulation of one-dimensional (1D) SL potentials in monolayer graphene produces ladder-like electronic energy levels near the Fermi surface, resulting in optical conductivity dominated by intersubband transitions (ISBTs). A specific and experimentally realizable platform comprising hBN-encapsulated graphene on top of a 1D periodic metagate and a second unpatterned gate is shown to produce strongly modulated electrostatic potentials. We find that Dirac electrons with large momenta perpendicular to the modulation direction are waveguided via total internal reflections off the electrostatic potential, resulting in flat subbands with nearly equispaced energy levels. The predicted ultrastrong coupling of surface plasmons to electrically controlled ISBTs is responsible for emergent polaritonic quasiparticles that can be optically probed. Our study opens an avenue for exploring emergent polaritons in 2D materials with gate-tunable electronic band structures.