It seems to me that there is a cluster of problems with this setup which need to be acknowledged.
1. Mini systems are a joke. Don't try to rationale it or anything else. The CRX-332 you linked to provides 20 watts of power at 10% distortion with a 6ohm load. It may not be stable at a 4 ohm load and will provide almost no power to a 16 ohm load. So, a far more serious amplifier is required (not optional) if any decent audio output is required.
2. Mini-systems are for mini rooms at low volume. In a family room with matching speakers, at reasonable volumes, this will sound much like any Bose system, but the outdoors, it turns out, are a great deal larger than most people's family room. Not only do you need good speakers outside, but the volume which would be very loud indoors, is somewhat quiet outdoors. You need far more volume to fill the space at even a reasonable level... Which leads back to issue #1.
3. 16 gauge cable won't be the issue. Anyone who is thinking this may be the issue is just not correct. 16 gauge cable won't deliver as well as 14 or 12 or 10 gauge, but is certainly plenty sufficient to deliver 100+ watts of power the distance required with almost zero loss in actual audio quality. Certainly not distortion.
4. The number one killer of speakers is under-powering them, and let me tell you, this is being done in spades with the current setup.
Solution:
Get a good amplifier! I really couldn't give two cents about the space requirements. If there isn't the space for the right product, then there isn't the right to complain about the stupid product which is being used. But, with some research you may be able to find a good amplifier for this setup.
Even something like this may be acceptable:
PyleHome - PAMP1000 - 160 Watt Home Stereo Power Amplifier
In the manual this unit will deliver 60 watts per channel into a 8 ohm load with .1% (not 10%!!!) THD. So, the specifications on this are light years ahead of the mini-system which was linked to.
You can hook up any iPod, or CD player or other audio source you would like to this amplifier and it includes front volume control and two sources which makes it a much better choice.
I'm sure people on these forums can give you much better alternatives to the thing I linked to which is generally low-end quality, but hopefully the point is clear - make room for a decent piece of gear to get good audio to the speakers outdoor.
Run separate speaker wire to each speaker. Not in series, not in parallel, but one wire pair per speaker. Preferably start with 14 gauge, but really, in my experience this doesn't matter in non-critical situations such as outdoors. What matters is having speakers which can fill the space with good audio.
Finally, 'Yamaha' speakers were mentioned, but they may be garbage or they may be excellent. Speaker quality always matters. Small 3" or 4" speakers aren't appropriate for any listening at serious volume and won't blend well with the outdoors at all.
People often have very unrealistic expectations of what they buy. They need to keep in mind the general rules: Smaller stuff is cute, but won't match up against the bigger stuff. You can pay more for smaller stuff which sounds worse than cheaper bigger stuff. Small speakers won't outperform similarly built larger speakers (typically), and outside, size and power matter a fair bit, because the size is so much greater.