So basically, your soundcard is only able to provide the audio signal to the 3.5mm jack. It is expecting that this signal will go into an amplifier of some sort before it is pushed to a speaker. This is typically the green wire from your sound card which goes to the sub-woofer for amplification. The amplified signal is then fed to your speakers.
In your case, the amplifier is on the Z623 sub-woofer or inside it. Most all PC sound cards are like this. Some have headphone amplifiers on them but it is rare to see a soundcard that has say a multi-channel amplifier(does one even exist?). They generate a lot of heat and the heat-sinks required, take up a lot of space. This is the reason most 5.1/7.1/9.1 home receivers have not gotten much smaller over the years. They are equipped with amplifiers so you can provide all your line level sources to it. It has the responsibility of all amplification and powering all of your speakers.
You don't have to use the subwoofer that came with the speakers but you do have to amplify this signal before it can be used by un-powered speakers.
You could get around this by buying some wireless speakers/Bluetooth speakers if you are trying to get sound from your laptop to somewhere that power is inconvenient. The speakers will need batteries for the same reason above....... they still receive only the line level signal and are amplifying this signal in its own internal amplifier before playing out. With Bluetooth speakers, you could even push content to them using your smartphone, instead of your laptop.