In this paper, we investigate into the functionality of the finite-tape information ratchet when its thermal transition is non-detailed balance. First, we construct an analytical framework of the information ratchet from stochastic thermodynamics by generalizing over that of [1] with detailed balance broken. This leads to special cases of the information processing first and second law stipulated by Semaan et al. [2] with the appearance of housekeeping heat. Through the application of Kullback-Leibler divergence as a statistical distance, we observe theoretically the mathematical condition for the finite-tape information ratchet to serve as an heat engine: its cumulative change in entropy should exceed that of the reduction in statistical distance of its initial to stationary state. While this is true for both the equilibrium and nonequilibrium stationary state, the heat extraction from the latter is exacerbated by the flow of housekeeping heat. We demonstrate the validity of our results by a Markov transition model which displays stochastic dynamics that is non-detailed balance.