This is just me kindof guessing off the top of my head, but:

• Depending where the mic is in relation to the keyboard, it can tell to some extent the relative distance from the key to the mic by volume of the keypress.
• The casing of the keyboard has a particular shape with particular acoustic properties which would make certain keys sound different than others. (Maybe the ones toward the middle have a more bass sound to them as opposed to more treble in the keys closer to the edges of the keyboard.)
• The surface on which the keyboard sits may also resonate differently with different keys.
• There may be some extent to which the objects in the room (including the typist and monitor, etc) could have reflected or absorbed soundwaves in ways that would differ depending on the angle at which the soundwaves hit them, which would be affected by the location of the key.
• Some keys like the spacebar and left shift almost always have a stabilizer bar which significantly affects the sound of the key for most keyboards.
• For human typists, there are patterns in the timing of key presses. It's quicker to type two keys in succession if those two keys are pressed by different fingers or different hands, for instance. Imaging typing the word "jungle", for instance. "J", "u", and "n" are all pressed with the right index finger (for touch typists). So the first three letters would be slower to type than the rest of the letters.
• I'd imagine this method also allowed the program to take into account various aspects of human language. (Probably English in this case, but it could just as well have been another language.) Certain strings of consonants just never appear consecutively. Certain letters are less frequently used. Things like that. Probably the accuracy would have been lower if the subjects were asked to type specific strings of random letters.
• It may also be that this particular experiment involved fairly controlled circumstances. They always placed the mic 12cm from the keyboard, for instance. Maybe they also used the exact same keyboard on the exact same desk with the exact same typist for all tests and training. And it sounds like they trained it on known text for a good while before testing the AI by asking the AI to actually discern what was typed. That's pretty perfect conditions that probably wouldn't be realistic for an actual attack. Not to minimize the potential privacy imacts of this, though. I'd fully expect methods like this to be more accurate for a more generalized set of cases.

Now, the researchers didn't sit down and list out all of these (or any other) ways in which software could determine what was typed from audio and compose an algorithm that accounted for all/most/some of these. They just kindof threw a bunch of audio with accompanying "right answers" at a machine learning algorithm and let the algorithm figure out whatever clues it could discern and combine those in whatever way it found most beneficial to come up with an (increasingly-more-accurate-with-every-training-set) answer. It's likely the algorithm came up with different things than I did that helped it determine which key(s) were being pressed.