We report on the observation of energy-resolved photoelectron (PE) spectra produced via two-extreme-ultraviolet-(XUV)-photon above-threshold ionization (ATI) of argon atoms. The XUV radiation consists of higher-order harmonics generated by the process of the relativistic oscillating mirror (ROM) in high-peak-power laser-pulse interaction with solid targets. The energetic XUV radiation is focused into an argon gas target at intensities high enough to induce two-photon ionization at yields that allow the recording of energy-resolved PE spectra. A clear two-XUV-photon ATI PE peak structure is observed in shot-to-shot measurements. This work is a first step towards a frequency-resolved optical gating-type characterization of attosecond pulse trains emanating from relativistic laser-plasma interactions and thus is important for XUV-pump-XUV-probe applications of these harmonics.