That depends. Some speakers draw very minimal power though the 3.5mm jack. Even though they do this it is extremely low draw, these are typically lower end too. Others simply use their own external power cable to wall socket.
The speaker wattage is maximum input of audio power they can handle. If your amplifier/receiver/tuner can deliver that kind of power they should handle up to 200 watts audio input power and, at that point, be really loud (probably distorted also) The 623's will draw almost all of their power from the built-in amplifier in the sub-woofer. which will draw its power from the wall socket.
The system will plug into your computer and the sound chip or sound card will use a small amount of power to send the signal to the input on the sub-woofer, and then it will be amplified and sent to the speakers. There will be very little draw from you computer system or power supply unit