We present Gemini GMOS-IFU data of eight compact low-mass early-type galaxies (ETGs) in the Virgo cluster. We analyse their stellar kinematics, stellar population, and present two-dimensional maps of these properties covering the central 5x 7 region. We find a large variety of kinematics: from non- to highly-rotating objects, often associated with underlying disky isophotes revealed by deep images from the Next Generation Virgo Cluster Survey. In half of our objects, we find a centrally-concentrated younger and more metal-rich stellar population. We analyze the specific stellar angular momentum through the lambdaR parameter and find six fast-rotators and two slow-rotators, one having a thin counter-rotating disk. We compare the local galaxy density and stellar populations of our objects with those of 39 more extended low-mass Virgo ETGs from the SMAKCED survey and 260 massive ($M>10^{10}$Msun) ETGs from the A3D sample. The compact low-mass ETGs in our sample are located in high density regions, often close to a massive galaxy and have, on average, older and more metal-rich stellar populations than less compact low-mass galaxies. We find that the stellar population parameters follow lines of constant velocity dispersion in the mass-size plane, smoothly extending the comparable trends found for massive ETGs. Our study supports a scenario where low-mass compact ETGs have experienced long-lived interactions with their environment, including ram-pressure stripping and gravitational tidal forces, that may be responsible for their compact nature.
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