We study the physical properties of a spectroscopic sample of 28 star-forming galaxies in a large filamentary structure in the COSMOS field at $z\sim$0.53, with spectroscopic data taken with the Keck/DEIMOS spectrograph, and compare them with a control sample of 30 field galaxies. We spectroscopically confirm the presence of a large galaxy filament ($\sim$ 8 Mpc), along which five confirmed X-ray groups exist. We show that within the uncertainties, the ionization parameter, equivalent width (EW), EW versus specific star-formation rate (sSFR) relation, EW versus stellar mass relation, line-of-sight velocity dispersion, dynamical mass, and stellar-to-dynamical mass ratio are similar for filament and field star-forming galaxies. However, we show that on average, filament star-forming galaxies are more metal-enriched ($\sim$ 0.1$-$0.15 dex), possibly due to the inflow of the already enriched intrafilamentary gas into filament galaxies. Moreover, we show that electron densities are significantly lower (a factor of $\sim$17) in filament star-forming systems compared to those in the field, possibly because of a longer star-formation timescale for filament star-forming galaxies. Our results highlight the potential pre-processing role of galaxy filaments and intermediate-density environments on the evolution of galaxies, which has been highly underestimated.