EXPLANATION:
This is a contract for publication of a story in a general-circulation magazine. The scope of "first-time rights" is unclear. It would cover first publication in one of the publisher's magazines, but it might also cover initial or subsequent publication in more than one of the publisher's magazines. It does not appear that the publisher is committing to publish the story in a particular magazine. If the magazines enjoy different levels of prestige, there is no guarantee that the story will appear in the high prestige publication rather than a lower prestige one. The author retains all other rights, including publication in or adaptation for other media .
The last clause is a grant back clause which gives the author rights that have been previously taken away. In this case, it allows the author to regain all rights in the work but this grant back is non-exclusive meaning the publisher retains the right to publish the work, including online.