The most frequently proposed model for the origin of quasars holds that the high accretion rates seen in luminous active galactic nuclei (AGN) are primarily triggered during major mergers between gas-rich galaxies. While plausible for decades, this model has only begun to be tested with statistical rigor in the past few years. Here, we report on a Hubble Space Telescope study to test this hypothesis for z = 2 quasars with high supermassive black hole masses ({M}{BH}={10}9{--}{10}10 {M}ȯ ), which dominate cosmic black hole growth at this redshift. We compare Wide Field Camera 3 F160W (rest-frame V-band) imaging of 19 point source-subtracted quasar hosts to a matched sample of 84 inactive galaxies, testing whether the quasar hosts have greater evidence for strong gravitational interactions. Using an expert ranking procedure, we find that the quasar hosts are uniformly distributed within the merger sequence of inactive galaxies, with no preference for quasars in high-distortion hosts. Using a merger/non-merger cutoff approach, we recover distortion fractions of {f}{{m},{qso}}=0.39+/- 0.11 for quasar hosts and {f}{{m},{gal}}=0.30+/- 0.05 for inactive galaxies (distribution modes, 68% confidence intervals), with both measurements subjected to the same observational conditions and limitations. The slight enhancement in distorted fraction for quasar hosts over inactive galaxies is not significant, with a probability that the quasar fraction is higher P({f}{{m},{qso}}\gt {f}{{m},{gal}})=0.78 (0.78σ ), in line with results for lower mass and lower z AGN. We find no evidence that major mergers are the primary triggering mechanism for the massive quasars that dominate accretion at the peak of cosmic quasar activity.