But that's exactly how I use "favorite". It's really useful, whether it's a cute picture I want to share with someone later or something more informative. "Like" does nothing for me; I don't always want to imply approval by clicking that button.
A long press on Twitter's native [Android] app and selecting "Share via..." will allow you to easily/quickly save it to Evernote (or whatever similar service you may use).
Personally I don't buy this. I'm used to 'favourites' and 'bookmarks' being used interchangably by browsers, which reduces the approval implication of that term... and the heart symbol doesn't mean 'like' to me, it means 'love', so has a higher level of implied approval than in your comparison.
The fact that they devoted an entire blog post to it makes me feel like they're headed in the wrong direction.
[1]: http://lowercasecapital.com/2015/06/03/what-twitter-can-be-2...