Using a combination of Hubble Space Telescope and James Webb Space Telescope imaging, a runaway supermassive black hole was recently identified with an inferred velocity of 954_{-126}^{+110}  km s^{-1}, likely ejected from a compact star-forming galaxy at z≈0.96. Assuming the runaway black hole originated from a gravitational-wave-driven merger of two supermassive black holes (SMBHs), we combine its measured recoil velocity with gravitational-wave recoil predictions from numerical relativity and black-hole perturbation theory to constrain the mass ratio and spin configuration of the progenitor binary that overcame the final-parsec problem and merged ∼70  Myr ago. We find that the progenitor binary must have been precessing, with a mass ratio m_{1}/m_{2}≲6, and that the more massive SMBH likely possessed a high dimensionless spin magnitude (∼0.75) in order to generate a recoil of this magnitude. Such SMBH mergers could represent an interesting source population for the upcoming Laser Interferometer Space Antenna mission, with characteristic signal-to-noise ratios of order ≳10^{3}. Furthermore, the inferred progenitor SMBH properties suggest that the compact galaxy likely originated from a major, gas-rich ("wet") merger between two galaxies of comparable mass, with a mass ratio ≲4.