It says right on the page that it's designed to work with 3 point belts and approved for use in a vehicle. So, I hope people realize it can't be used on an airplane.
That being said, the web site *implies* airplane use by stating how great it is for travel and even showing an airplane in their video. They mean to take with you to destinations, but to consumers, it appears it can be used on an airplane. Also, they don't appear to explicitly state that it is not approved for airplane use. In their FAQ they have a page that shows each countries rules for whether or not car seats can be used on the plane. Why bother with that if this isn't approved for airplane use? Just tell people that. Making them read the rules is just going to confuse them.