For [1] to work, you need to either run the bookmarklet or Chrome extension. This isn't the norm though; most annotated pages can be viewed directly from the genius link, and you can even link directly to a specific annotation, for example [3].
[1]: https://www.bloomberg.com/graphics/2015-paul-ford-what-is-co...
[2]: https://genius.com/summary/www.bloomberg.com%2Fgraphics%2F20...
[3]: http://genius.it/7163911/www.theverge.com/2015/6/24/8836087/...
They tried dirty SEO tactics that Google ultimately punished them for, and their staff have made off-color remarks in the past. There's a lot more if you search for it.
http://www.recode.net/2014/5/26/11627246/rap-genius-co-found...
Things at Genius have been pretty controversy-free since 2014.
And if Genius is hosting the page that's annotated, that's one thing. If they're simply proxying it on demand and adding annotations, then I don't see how it violates copyright unless every proxy server violates copyright.
This is a key distinction that separates proxies from caches and archives.