If the amp really takes in high level inputs then I would say to just use this amp. It should work fine. It's four channels so it's perfect for your stock amp. Because of the way it connects to everything makes it simple. There's no special connectors or anything needed so you can just cut the wires on your stock wiring harness and plug them in. The only real issue I see with this is that you'll be buying and 200 watt amp just to supply signal to a factory 180 watt amp. If you do decide to go this route be sure to find a heatsink for the chip.
I'm sure you could probably use the amp you posted but powering it may be an issue. I don't know what kind of voltages it operates on but I'm sure that it probably runs on the 12 volt system and can be operated of of the computers power supply.