First off, I didn't really mess with my stock speakers for very long.
I'm almost certain that the 'Left front speaker' wire in the harness is somehow wired to a crossover or is eventually split and resistors are used for the tweeters and the woofers, so to answer your question: an amp is not required, the speakers are powered through the harness you will have to connect to your existing wires and eventually to your headunit.
The powered outputs you see are used when you've got an amp. If you decide to buy an amp, make sure it has a sub-out as well, in case you plan to add one in the future. Here's how your wiring will work:
Headunit --(RCA cables)--> Amp --(Spkr wire)--> Crossover IN
Then from there you have two separate outputs from your crossover, one set of speaker wires for your tweeters, and another for your woofers.
Hope that helps.
Edit: For clarity, he's a pic of the back of a generic HU:
The black female connector (swear I'm not racist!
) is where the new harness will plug into, after you solder or crimp the existing wires to it. Those wires will include the wires that run to all of your speakers.
Now, if you CHOOSE to utilize an amp, you will use the RCA outputs seen in the set of 3. (Front, Rear, Sub) If you go this route, you will have to re-wire your speakers.