We contrast the gas kinematics and dark matter contents of $z=2$ star-forminggalaxies (SFGs) from state-of-the-art cosmological simulations within the$\Lambda$CDM framework to observations. To this end, we create realistic mockobservations of massive SFGs ($M_*>4\times10^{10} M_{\odot}$, SFR$>50~M_{\odot}$ yr$^{-1}$) from the TNG50 simulation of the IllustrisTNG suite,resembling near-infrared, adaptive-optics assisted integral-field observationsfrom the ground. Using observational line fitting and modeling techniques, weanalyse in detail the kinematics of seven TNG50 galaxies from five differentprojections per galaxy, and compare them to observations of twelve massive SFGsby Genzel et al. (2020). The simulated galaxies show clear signs of discrotation but mostly exhibit more asymmetric rotation curves, partly due tolarge intrinsic radial and vertical velocity components. At identicalinclination angle, their one-dimensional velocity profiles can vary alongdifferent lines of sight by up to $\Delta v=200$ km s$^{-1}$. From dynamicalmodelling we infer rotation speeds and velocity dispersions that are broadlyconsistent with observational results. We find low central dark matterfractions compatible with observations ($f_{\rm DM}^v(<R_e)=v_{\rmDM}^2(R_e)/v_{\rm circ}^2(R_e)\sim0.32\pm0.10$), however for disc effectiveradii $R_e$ that are mostly too small: at fixed $R_e$ the TNG50 dark matterfractions are too high by a factor of $\sim2$. We speculate that thedifferences in gas kinematics and dark matter content compared to theobservations may be due to physical processes that are not resolved insufficient detail with the numerical resolution available in currentcosmological simulations.