Your calculation is probably using the standard rectilinear lens formula, which assumes straight lines stay straight. With a 1/4" sensor and 2.8mm focal length, that gives a much smaller horizontal/vertical angle of view, and even the diagonal angle is only around 77°.

So if the specs claim 120°, that angle is likely not for a rectilinear lens. It usually means the lens has strong barrel distortion or is fisheye-like, where the normal focal-length/angle-of-view formula does not apply.

In short: you’re not necessarily doing the math wrong—the published 120° spec is likely measured using a distorted wide-angle/fisheye projection, not the standard rectilinear one.