Spectral observations of the type-IIb supernova (SN) 2016gkg at 300-800 days are reported. The spectra show nebular characteristics, revealing emission from the progenitor star's metal-rich core and providing clues to the kinematics and physical conditions of the explosion. The nebular spectra are dominated by emission lines of [OI]{lambda}{lambda}6300,6364 and [CaII]{lambda}{lambda}7292,7324. Other notable, albeit weaker, emission lines include MgI] {lambda}4571, [FeII]{lambda}7155, OI{lambda}7774, CaII triplet, and a broad, boxy feature at the location of H{alpha}. Unlike in other stripped-envelope SNe, the [OI] doublet is clearly resolved due to the presence of strong narrow components. The doublet shows an unprecedented emission line profile consisting of at least three components for each [OI]{lambda}6300,6364 line: a broad component (width ~2000km/s), and a pair of narrow blue and red components (width ~300km/s) mirrored against the rest velocity. The narrow component appears also in other lines, and is conspicuous in [OI]. This indicates the presence of multiple distinct kinematic components of material at low and high velocities. The low-velocity components are likely to be produced by a dense, slow-moving emitting region near the center, while the broad components are emitted over a larger volume. These observations suggest an asymmetric explosion, supporting the idea of two-component ejecta that influence the resulting late-time spectra and light curves. SN 2016gkg thus presents striking evidence for significant asymmetry in a standard-energy SN explosion. The presence of material at low velocity, which is not predicted in 1D simulations, emphasizes the importance of multidimensional explosion modeling of SNe.