The rotational and translational dynamics of molecular hydrogen trapped within β-hydroquinone clathrate (H_{2}@β-HQ)-a practical example of a quantum particle trapped within an anisotropic confining potential-were investigated using inelastic neutron scattering and Raman spectroscopy. High-resolution vibrational spectra, including those collected from the VISION spectrometer at Oak Ridge National Laboratory, indicate relatively strong attractive interaction between guest and host with a strikingly large splitting of rotational energy levels compared with similar guest-host systems. Unlike related molecular systems in which confined H_{2} exhibits nearly free rotation, the behavior of H_{2}@β-HQ is explained using a two-dimensional (2D) hindered rotor model with barrier height more than 2 times the rotational constant (-16.2 meV).