The shape of a galaxy's spatially unresolved, globally integrated 21-cm emission line depends on its internal gas kinematics: galaxies with rotationally supported gas discs produce double-horned profiles with steep wings, while galaxies with dispersion-supported gas produce Gaussian-like profiles with sloped wings. Using mock observations of simulated galaxies from the FIRE project, we show that one can therefore constrain a galaxy's gas kinematics from its unresolved 21-cm line profile. In particular, we find that the kurtosis of the 21-cm line increases with decreasing V/σ and that this trend is robust across a wide range of masses, signal-to-noise ratios, and inclinations. We then quantify the shapes of 21-cm line profiles from a morphologically unbiased sample of ~2000 low-redshift, HI-detected galaxies with M star = 107-11 M☉ and compare to the simulated galaxies. At M star ≳ 1010 M☉, both the observed and simulated galaxies produce double-horned profiles with low kurtosis and steep wings, consistent with rotationally supported discs. Both the observed and simulated line profiles become more Gaussian like (higher kurtosis and less-steep wings) at lower masses, indicating increased dispersion support. However, the simulated galaxies transition from rotational to dispersion support more strongly: at M star 108-10 M, most of the simulations produce more Gaussian-like profiles than typical observed galaxies with similar mass, indicating that gas in the low-mass simulated galaxies is, on average, overly dispersion supported. Most of the lower-mass-simulated galaxies also have somewhat lower gas fractions than the median of the observed population. The simulations nevertheless reproduce the observed line-width baryonic Tully-Fisher relation, which is insensitive to rotational versus dispersion support.