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We present a study of the molecular gas of seven early-type galaxies withhigh angular resolution data obtained as part of the mm-Wave InterferometricSurvey of Dark Object Masses (WISDOM) project with the Atacama LargeMillimeter/submillimeter Array. Using a fixed spatial scale approach, we studythe mass surface density ($\Sigma$) and velocity dispersion ($\sigma$) of themolecular gas on spatial scales ranging from $60$ to $120$pc. Given the spatialresolution of our data ($20$ - $70$pc), we characterise these properties acrossmany thousands of individual sight lines ($\approx50,000$ at our highestphysical resolution). The molecular gas along these sight lines has a largerange ($\approx2$dex) of mass surface densities and velocity dispersions$\approx40\%$ higher than those of star-forming spiral galaxies. It has virialparameters $\alpha_\mathrm{vir}$ that depend weakly on the physical scaleobserved, likely due to beam smearing of the bulk galactic rotation, and isgenerally super-virial. Comparing the internal turbulent pressure($P_\mathrm{turb}$) to the pressure required for dynamic equilibrium($P_\mathrm{DE}$), the ratio $P_\mathrm{turb}$/$P_\mathrm{DE}$ is significantlyless than unity in all galaxies, indicating that the gas is not in dynamicequilibrium and is strongly compressed, in apparent contradiction to the virialparameters. This may be due to our neglect of shear and tidal forces, and/orthe combination of three-dimensional and vertical diagnostics. Both$\alpha_\mathrm{vir}$ and $P_\mathrm{turb}$ anti-correlate with the globalstar-formation rate of our galaxies. We therefore conclude that the moleculargas in early-type galaxies is likely unbound, and that large-scale dynamicslikely plays a critical role in its regulation. This contrasts to the giantmolecular clouds in the discs of late-type galaxies, that are much closer todynamical equilibrium.

WISDOM Project -- XVII. Beam-by-beam Properties of the Molecular Gas in Early-type Galaxies