The other speakers are NOT powered. Yes, you will need some sort of amplifier, most typically a receiver. If you were capable of adding an audio out plug from the typical just a few to 15 watts built in amp for audio, the signal would be insufficient to run the external speakers. The TV tuner is your video "receiver."

As to how to connect, visit the very welcome, which will make it easy for a person like you who may tend to jump to conclusions.

Some fundamentals include the idea that HDMI is a one wire connector which conveys both video & audio.

Now, there are a few alternatives when it comes to wiring the connections. Especially when blessed with plenty of HDMI connectors, some of us prefer to connect the disk player directly to the TV instead of by way of going through the receiver. Typically, TVs may do a better job of processing the signal rather than possibly introduce problems by going through the receiver as another device that may add video "noise" by imperfect processing. From the TV, the audio output signal will be amplified for the speakers (with exception of the self powered sub woofer.)

The audio out of the disk player must be routed through an amplifier. The disk player cannot have wires from it directly to the speaker set. That situation has no amplification for the audio. As an aside, if your amp would be, say a 5.1 configuration, you cannot get 7.1 out of it because, by definition it only has enough amplification channels for 5.1.