Some types of intolerance can be diagnosed that way. If I recall correctly it mainly works for different types of sugar:
After ingesting a specific amount of sugar (let’s say 25g of lactose dissolved in warm water), you take measurements of H
2 concentration in the air you breath out. For sugar types you can not metabolize, there will be a spike in H
2 concentration, because bacteria in the colon will produce H
2 gasses that are dissolving into the blood stream and finally exhaled.
The whole procedure takes several hours for each type of sugar you want to test.
After looking at the FAQ, that seems exactly what the AIRE is measuring.
In general, I don’t think this device will be of much use, because figuring out what exact type of »XYZ« you can not metabolize is a real PITA.
If you eat a regular meal and use this device the collected data will be almost useless garbage, because you would need to individually test each and every component of that meal, down to the different sugars, fiber, proteins...
In that regard, your gut-feeling will be of the same use - if not better.
Eat whole foods, drop the pre-processed crap and junk food and your body will tell you what it needs
In short: The AIRE is just another piece to throw on the ever growing pile of "smart garbage" no one needs and no one should spend money on.