SoundFlower does this, it's open source. It contains a decent chunk of audio routing features that are inexplicably missing from the core OS X.

For instance, you can route application audio out to a Soundflower channel and use that as input for another app.

Edit: just checked, Soundflower rerouting works perfectly with the Shazam Mac app, tried it out on a couple of YouTube songs, and it got it right on 47 out of the current top 50. It's a shame that Shazam is still only useful for mainstream stuff, when I tried it on some random metal, Goa, soundtracks, and industrial... 0 out of 15.

http://audentifi.com does this :)

I must have skipped over the article as I assumed it could pick up on internal audio. Seems like an oversight...

You can do this (and a ton of different cool stuff) with RogueAmoeba's Audio Hijack Pro app, which lets you route audio from one app to another, optionally applying some filters to it. I sometimes use it to fix audio out-of-sync problems in certain videos.

Edit: As commenter above noted, the audio routing functionality is also available with the free Soundflower app.

Assuming you have the volume up, why can't it pick that up from the speaker?

Well it's definitely picking up what I'm listening to on both Spotify and Youtube with my headphones on.