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Recently synthesized two-dimensional graphene-like material referred to as graphenylene is a semiconductor with a narrow direct bandgap that holds great promise for nanoelectronic applications. The significant bandgap increase can be provided by the strain applied to graphenylene crystal lattice or by using nanoribbons instead of extended layers. In this paper, we present the systematic study of the electronic, optical and thermoelectric properties of graphenylene nanoribbons using calculations based on the density functional theory. Estimating the binding energies, we substantiate the stability of nanoribbons with zigzag and armchair edges passivated by hydrogen atoms. Electronic spectra indicate that all considered structures could be classified as direct bandgap semiconductors. The absorption coefficient, optical conductivity, and complex refractive index are calculated by means of the first-principles methods and the Kubo-Greenwood formula. It has been shown that graphenylene ribbons effectively absorb visible-range electromagnetic waves. Due to this absorption the conductivity is noticeably increased in this range. The transport coefficients and thermoelectric figure of merit are calculated by the nonequilibrium Green functions method. Summarizing the results, we discuss the possible use of graphenylene films and nanoribbons in nanoelectronic devices.