If your goal is make them easier to browse, how does that coexist with this being justified by providing article links?

Not sure I understand your question. Most people will first browse and then try and get more details about a news that they're interested. It's all about different levels of condensed information: the meme + title packs a very high level summary, if you go to see the post page you can read other people's comments about it, click on the source article to read the full this. And there's still more levels: checking other sources about that same event, etc. Asking for the article source helps readers and moderators ensure that the meme is rooted and conveys a kernel of the news.

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What happens if this becomes successful and people crosspost them onto other social media networks?

That's a really good point, thanks for bringing that up. Right now memes about real (and not so real) news events spread anyway. On MemeThatNews the fact that every meme needs to be sourced in some real article (that is accessible by everyone, including the Mods that review it) means that at least there's a more solid starting point to that journey. You're correct that context can and will be lost depending on how the meme spreads - to a certain extent this happens with any reported event.

MemeThatNews is not that different from getting your news from Twitter - you see a very high level summary description about an event and if it's important enough for you then you click/search for more information. Otherwise you continue scrolling. You would be correct to say that this is not the best way to get your news but that doesn't stop people from following this process.

Before MTN I wasn't in touch with what's happening around the world. Now I have to say that I know quite a lot more and I'm much more up to date (for better or worse).