A hybrid spin-electron system defined on a one-dimensional double-tetrahedral chain, in which the localized Ising spin regularly alternates with two mobile electrons delocalized over a triangular plaquette, is exactly solved with the help of generalized decoration-iteration transformation. It is shown that a macroscopic degeneracy of ferromagnetic and ferrimagnetic ground states arising from chiral degrees of freedom of the mobile electrons cannot be lifted by a magnetic field in contrast to a macroscopic degeneracy of the frustrated ground state, which appears due to a kinetically driven frustration of the localized Ising spins. An anomalous behavior of all basic thermodynamic quantities can be observed on account of massive thermal excitations, which mimic a temperature-driven first-order phase transition from the nondegenerate frustrated state to the highly degenerate ferrimagnetic state at nonzero magnetic fields. A substantial difference in the respective degeneracies is responsible for an immense low-temperature peak of the specific heat and very abrupt (almost discontinuous) thermal variations of the entropy and sublattice magnetizations.