  The shape of a galaxy's spatially unresolved, globally integrated 21-cm
emission line depends on its internal gas kinematics: galaxies with
rotation-supported gas disks 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 $V/\sigma$, 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 $\sim$2000 low-redshift, HI-detected
galaxies with $M_{\rm star} = 10^{7-11} M_{\odot}$ and compare to the simulated
galaxies. At $M_{\rm star} \gtrsim 10^{10} M_{\odot}$, both the observed and
simulated galaxies produce double-horned profiles with low kurtosis and steep
wings, consistent with rotation-supported disks. 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 rotation to dispersion support
more strongly: at $M_{\rm star} = 10^{8-10}M_{\odot}$, 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 rotation vs. dispersion support.
