Haven't done what you're doing but I currently have the basic Kicker set-up driving six speakers as it came from the factory. As such, I'm thinking you should be good to go without additional amplification. However, I'm sure someone that really knows will chime in.
If you add two more speakers in parallel with the existing ones you will be placing a 2 ohm load on each channel, assuming all speakers are 4 ohm ( industry standard). Most likely you will cause the radio's amplifier to go into thermal shutdown at high levels as you would double the heat inside the radio. Of course you could switch to all 8 ohm speakers and connect as you say but an inexpensive 2 channel amp to drive the extra speakers would be a cheaper way to go. Also switching to 8 ohm speakers will cut your output level in half at each speaker theoretically and alllow the parallel wiring connection. A third option would be to connect two speakers on each channel in series which would allow you to use 4 ohm speakers and making the load on the radio 8 ohms. Again half output power meaning it won't be as loud. This configuration can cause some funky phasing issues but probably not noticeable on a boat. Any radio that is running off of 12v is only capable of about 20 Watts RMS per channel. You hear so many gimmicks of how power is rated, my favorite is peak power which is nearly useless so be careful when you shop for speakers or an amp. The large expensive amps have internal D.C. To D.C. Power supplies to step up the voltage and those are capable of very high power levels but the speakers should be capable of handling it. Look for products that are rated in RMS power so you know what your getting and can do direct comparisons. There is a lot more to this like distortion and efficiency so let me know if you need help picking anything out or a wiring diagram.
Those plugs are inputs for an amp. They won't power a speaker. If you piggybacked off the other speaker, try disconnecting the other speakers and see what happens.
When you say you "spliced" into the wire, did you just cut one of the +/- joined wires and add in another +/-? Or did you run it from the speakers tabs? Did the speaker you tapped into also lose sound, or does it sound the same as before?
How many speakers did you originally have on your boat?
And yes Carl is right, the RCA'S are your pre-out for an amp.
Hmm, so I looked at the link you provided earlier, I see it says 4-6 Ohm. What does it say on the back of the speaker? I'm almost wondering if it is a 6 Ohm speaker, than the path of least resistance would be through the factory 4 Ohm speaker, which I believe would be why you would be getting almost no sound from the add on speakers. If I remember my physics right. I would try just disconnecting the factory speaker and see what happens.
I could be way off base here too, probably someone smarter than me can correct if my thinking is incorrect.
