You can't typically drive speaker selectors with more than about 100 watts per channel. This one claims about 200 watts, then confuses itself back to 100... So, hard to be sure.
I would use an amplifier like this one:
http://www.ebay.com/itm/Sonance-275-SE-2-channel-amplifier-/232343014015?hash=item3618b90a7f:g:1tIAAOSwhvFZDeJy
You can see in the photos the standard RCA inputs, and then the amplified speaker outputs on the back.
How do you intend to control volume in all those places? You typically need volume controls in line to allow for volume to be adjusted up/down in every location.
Personally, I would likely have gotten a speaker selector/volume control integrated unit which does the same thing as what you have, but adds volume control for the different audio zones.