He's definitely not heating it to a boiling temperature. Boiling MAKES its own air. That's the definition of vaporization.
Now, with the cap closed, the boiling temperature under pressure will be higher than 100 degrees Celsius. But if the plastic bottle doesn't explode before visible gas is produced, you WILL be able to see visible gas.
If he were to have heated to 1atm boiling temperature, there would have been an instant rush of bubbling, and the scalding water will jet/gush out of the bottle when he opened the cap (as a shaken bottle of soft drink would).