Smallest dpi and size face image identifiable by AI?

Unless the AI has a hard-wired cutoff - which would be reasonable, because its engineers don't want it coughing out too many false matches - this will be a giant mess of probabilities. There are more metrics for image quality than pixel count. And that's before you get to the lighting on the subject, angle the image was taken from, clothing & hair, etc. Add how distinctive the person's face is. And the quality of your match set images. And the size of those match sets - are you asking the AI "is this one of the 5 Pete's Pizza delivery drivers, to unlock the back door for him?" Or asking it "who is this unknown person in NYC?".

And how sure do you want this "positive" match to actually be? The back door at Pete's Pizza is (probably) far lower stakes than a murder conviction.

There's more to it than resolution. The systems I work on recognize fine features of objects at high speed. Not facial recognition, but similar. One of those systems has an imaging sensor similar to the one you mentioned.

It works quite well, in part because the camera is optically excellent, in part because it provides rich and accurate color data, and in part because we tightly control the environment that the image is captured in.

In a less controlled environment, or if using lower quality sensors or optics, the results would be poor.