Byteball didn't have mining nor an ICO. Byteball team premined the entire supply and decided to airdrop them to Bitcoin holders and also to some other communities.
But they still have about 35% that isn't distributed yet. So, they want to airdrop it in a way that brings value to their coin but also has a fair distribution to ensure decentralization. That's why they decided to airdrop to steem users.
Byteball's team member @punctured recently hinted in a reply to me about that:
All investors in Byteball are aware of the undistributed funds, and that all of it is to be distributed for free. I am sure that when the dust settles, this Steem campaign will have proven to be far more valuable than the initial airdrops to BTC holders. We have already seen impressive amount of content being created and people engaging on Byteball communities. Needless to say, some of the exploits caught the attention of developer communities like thebot.net and Utopian. Having developers become aware of a platform allowing anyone to build on top of it really isnt all that bad.