Blimey! Point 10 is worth reading. The sublicencing clause would bother me a bit. It could hypotheically mean they could licence your work to the Daily Mail (or any other publication) for a nice profit. However, I think the intention is only that it means they can use it across different Medium platforms for promotional purposes.

10. License to Submission: By entering the Contest and providing your Submission in connection with the Contest, you hereby grant to Sponsor, for a period of 1 (one) year after the end of the Contest Period, an irrevocable, nonexclusive, royalty-free, worldwide, fully paid, and sublicensable license to use, reproduce, modify, adapt, publish, translate, create derivative works from, distribute, publicly perform and display your Submission, in any manner or media now known or later developed on Medium.com (continued...)