I'm not a fan on 9gag, but I can understand why they wouldn't want to work with you. There are many issues with just having some random guy - despite how good natured he is - in charge of your company's official app.
They're asking ruqqq to stop infringing on their trademark and copyright, not necessarily stop development.
The trademark issue is likely resolvable by removing the "9GAG for Android" tagline and any other implied or expressed official connection to 9GAG that might appear in the app, website, or other marketing materials.
What they're referring to with regards to the copyright violation is a little more complex: are they referring to the user-supplied content? Did ruqqq use 9GAG creative in the app? Something else? If it's anything other than the user-supplied content, which 9GAG doesn't have a copyright on anyway, that should be relatively straightforward to resolve, as well.
But GP is referring to ruqqq's implied offer to make Nine the official 9GAG app (at least in some capacity), not that ruqqq actually is, at this moment, in charge.
The email clearly states "using our trademark and CONTENT". That's what the email is for. Furthermore, their TOS is worded to be confusing (at least it is to me): http://9gag.com/tos
Anyhow, I'm not going to make this into im-a-bitter-dev commotion. Some here even state that it's not the users I'm worried about because if I am, then I can just direct them to the official app.
My real concern is that my app existed before 9GAG's, and although 90% of my users are using it free, there are some who appreciate the work I put into making a nice-to-use app and bought the "Pro" version. These are the people I would NOT want to disappoint. I'm still weighing solutions and brainstorming on how to make their dollar spent worth it. But for now, I've removed 9GAG references in the Play Store listings.
Their TOS does not claim ownership over user-supplied content; see section 2, "All materials displayed or performed on the Site[...](other than Content posted by Subscriber (“Subscriber Content”)) are the property of 9GAG, Inc[...]" and section 3, "Subscriber shall own all Subscriber Content that Subscriber contributes to the Site[...]".
The letter does claim that you are using their content, but the use of which infringes on their trademark and copyright. Your use of the user-submitted content would not infringe on their copyright: users were never asked to assign copyright to 9GAG, and in most cases, would not be able to as they were not the original copyright holders to begin with.
If there was a fundamental copyright problem (i.e., the entire basis of your app is copyright infringement due to an ownership claim on all the user-supplied content) and they wanted to shut your app down, they could've just issued a run-of-the-mill DMCA takedown notice to Google. That they didn't seems, to me, that they are fine with your app as long as you remove the infringing elements.
If you were interested in keeping Nine around without fear of 9GAG taking additional action, I'd ask them what content, exactly, infringes on their copyright and have them enumerate what you need to remove. It may be something relatively straightforward, like certain assets or logos that you may be using in your app.
Yes, I agree if ruqqq brands it as just-another-funny-app then perhaps there won't be any copyright violations, since 9GAG steals content from other sites, stealing content from them won't amount to any copyright violation. In my opinion unless 9GAG specifically says that the user-supplied content belongs to them, then it doesn't, but the terms here say something on those lines: http://9gag.com/tos
Their TOS makes it pretty clear that the user-supplied content doesn't belong to them, under section 3 "Subscriber Content":
> Subscriber shall own all Subscriber Content that Subscriber contributes to the Site, but hereby grants and agrees to grant 9GAG, Inc a non-exclusive, worldwide, royalty-free, transferable right and license (with the right to sublicense), to use, copy, cache, publish, display, distribute, modify, create derivative works and store such Subscriber Content and to allow others to do so (“Content License”) in order to provide the Services.
And under section 2 "Site Content", they claim ownership of everything except user-generated content (emphasis here is mine):
> All materials displayed or performed on the Site, including, but not limited to text, graphics, logos, tools, photographs, images, illustrations, software or source code, audio and video, animations and Themes (as defined below), including without limitation the 9GAG, Inc Template Code (as defined below) (collectively, “Content”) (other than Content posted by Subscriber (“Subscriber Content”)) are the property of 9GAG, Inc and/or third parties and are protected by Hong Kong and international copyright laws.
Even if they did try claim ownership, one can't transfer a copyright they don't hold, which is the case for most of 9GAG's user-supplied content.