Vortex coronagraphs have been shown to be a promising avenue for high-contrast imaging in the close-in environment of stars at thermal infrared (IR) wavelengths. They are included in the baseline design of the mid-infrared extremely large telescope imager and spectrograph. To ensure good performance of these coronagraphs, a precise control of the centering of the star image in real time is needed. We previously developed and validated the quadrant analysis of coronagraphic images for tip-tilt sensing estimator (QACITS) pointing estimator to address this issue. While this approach is not wavelength-dependent in theory, it was never implemented for mid-IR observations, which leads to specific challenges and limitations. Here, we present the design of the mid-IR vortex coronagraph for the “new Earths in the α Cen Region (NEAR) experiment with the Very Large Telescope (VLT)/Very Large Telescope imager and spectrometer for the mid-infrared (VISIR) instrument and assess the performance of the QACITS estimator for the centering control of the star image onto the vortex coronagraph. We use simulated data and on-sky data obtained with VLT/VISIR, which was recently upgraded for observations assisted by adaptive optics in the context of the NEAR experiment. We demonstrate that the QACITS-based correction loop is able to control the centering of the star image onto the NEAR vortex coronagraph with a stability down to 0.015 λ  /  D rms over 4 h in good conditions. These results show that QACITS is a robust approach for precisely controlling in real time the centering of vortex coronagraphs for mid-IR observations.