If you don't want to use USB soundcard, you're probably SOL.
What you have is a 5.1 sound setup based on three stereo wires - left/right front, left/right rear and center/sub. This is the setup used mainly by Creative, the biggest maker of sound boards on the PC side, that has since spread to be included on many motherboards. It relies on analog audio being sent to speakers with included amplifiers. The Mac uses the same setup as DVD-players, where the compressed digital audio is sent to a receiver which then decodes and amplifies the sound before sending it to the speaker. Modern PC motherboards often support both methods, but the 3 stereo plugs is the most commonly used.
The advantage of the Mac/DVD way of doing it is that the sound quality is much higher, since you're never sending unamplified analog audio outside the receiver. The downside is for realtime 5.1 sound - ie games - which has to be compressed and encoded on the fly to be sent to the receiver (for DVDs this is not an issue - the sound is compressed on the DVD and is just passed on to the reciever). This is doable using so-called Dolby digital live, but the chips are still slightly expensive, and Creative tries to stop its spread at every turn, including buying up and shutting down competitors that use it. This way people have to buy "PC speakers" (like you just did) for their PCs instead of using home theater systems. Creative is big on PC speakers and a nobody on the receivers, so they like the current setup.
What you need is something that puts out unamplified 5.1 sound over 6 wires or 3 stereo wires. A receiver won't really help you - some high-end receivers do support sound in over 6 wires, and you could use that if you don't mind having two volume controls, but they tend to be expensive. A USB plug would be cheaper. While you could in theory make an external decoder and plug it into the Mac's optical audio out, I'm aware of no such gadget (and yous till wouldn't get 5.1 sound from games). What you need is to either get a USB plug, or get a receiver and speakers separately and forget about the Logitech ones. The first is better for gaming, if you play games that support 5.1 sound, and the second is better for music and DVDs. Your call.
Of course, you can still plug in just two speakers and get regular stereo sound, but I guess that that's not what you're after.
EDIT: Sorry, made a mistake. You have one wire out and six wires in (on the speakers), not the other way around. You can in fact use a regular receiver - it's unlikely that you'll find one with stereo plugs for the sound out, but there are adapters to for instance RCA plugs. Best way then is to set the speakers to a consistent volume and use the receiver for the volume control. You will get the worst of both worlds - no 5.1 sound from games and lower audio quality - but it is doable.
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