Before you enter the memotions contest...
This is the grant of rights you're signing. I've chopped out the less concerning bits and bolded and italicized the red-alert phrases. Translation below.
Each Entrant shall retain its ownership interest in and to its Entry. However, in consideration for the opportunities provided herein, each Entrant (or, in the event the Entrant is a minor, the Entrant’s respective parent or legal guardian) hereby grants Sponsor, and its agents, affiliates, successors, and assigns, a perpetual, irrevocable, universal, non-exclusive, fully-paid and royalty-free, sub-licensable and transferable license to use, edit, modify, distribute, and commercially exploit the Entry in any manner and for any purpose.
...Sponsor reserves the right, but not the obligation, to use the Entry for any purpose, including, but not limited to, posting, commercial sales, reproduction, disclosure, advertising and promotional activities, distribution, transmission, publication, and broadcast. Sponsor reserves the right to use any ideas, concepts, knowledge, or techniques contained in the Entry for any purpose, including, but not limited to, developing and marketing products and/or services using such information, and each Entrant acknowledges and understands there shall be no further payment, consideration, royalties or other compensation from Sponsor, its agents, affiliates or assigns for any use of said Entry or the content therein pursuant to this Grant of Rights.
... In the event an Entry is deemed a prize winner of this Contest, the Entrant further agrees that it shall not seek to market, distribute, sell, sublicense, or otherwise commercially exploit the Entry in any form or manner without the express prior written permission of the Sponsor.
For those who may not have spent several years following publishing news, this is a very concerning grant of rights. In plain English, it means once you enter, Riot has the right to do WHATEVER THEY WANT with your work, up to and including selling it. Even if you don't win. And you get nothing, and they owe you nothing. (Oh, if you don't win, you can attempt to publish/submit it somewhere else. I guess that's something.)
Why is this important? Well, think about what the contest is asking for. Look at the art at the top of the page. Riot is basically asking you to design emotes. And if they like it, and other people like it (the first round of judging is a popularity contest), then they can do what they want with it, including "commercially exploit it"--that is, sell it as a real emote in the shop for real RP, without paying you even with a copy of the emote.
Will they do that? We don't know. But according to the entry rules, they have the RIGHT to do it. And that's concerning. The contract isn't there for when everything is going fine. The contract is there for when $#!+ hits the fan. The contract should be read and agreed to as though ten minutes after signing, both parties will be hit by a truck, and the fallout will be negotiated by your vindictive next-of-kin, who hate both you and each other.
Now, you may not consider this a problem. Maybe you don't like emotes anyway, so getting one for free doesn't matter to you even if you designed it. Maybe, since it's fanart and some people can knock this stuff out in ten minutes or less, the effort it takes you is little enough you don't mind. Maybe it's worth it to you to just have people look at your art.
But you have to understand. I don't want anyone going in blind. If you decide to do it anyway, that's okay. But really ask yourself, in the absolute best case scenario, where you win, are you okay with never posting this? With never sharing it? And in the absolute worst case, where you win and Riot exploits all the rights in this, are you okay with potentially seeing that emote in the store, which you can't afford/don't want to pay for, knowing that you signed away the right to argue?