What is the legal qualification of an airdrop?

This largely depends on the contractual setup of the airdrop as well as on the utility
connected to the airdrop.
The airdrop can be a gift if it is free for the recipient who doesn’t have to do anything specific
to receive the airdrop.
However, airdrops are sometimes used as a kind of incentive to motivate holders of a NFT
project to do something. For example, the airdrop is promised in the roadmap to minters of
the project. In such a case, the airdrop is more than just a gift. Instead, it is part of the actual
(sales) contract of the NFT – the minters do not only buy the original NFT, but also the
airdrop that is promised to them and that becomes part of the contract.
And in addition to the contract related to the airdrop token itself, the contract related to the
utility of the airdrop needs to be considered, too. For example, if the utility of the airdrop is a
picture (or access to other media, such as a movie or music track), the contract of the airdrop
might include some sort of a licensing deal, especially in the form of usage right related to
the connected media. Other airdrops might be some form of vouchers that enable their
holders to trade the vouchers into something else later, e.g., physical items such as t-shirts,
printed art works or books.