I think what is being said there if I am not mistaken is in two parts

1. Emphasising that your API should be used for assets you have control over i.e those ones that are your own and not those in your reach as a custodian. Its just a way to hammer it to those who have been using it for such purpose which I am sure is something that would have been in the terms and conditions of its use.

2. The second part is just telling the other use of the API and how it can be used on mobile for the same purpose its used on the web. Its as simple as that. But if all this does not apply to you, you don't need to act on it.