I used to use one of those ATI All-In-Wonder cards for this. It has a device similar to the one you linked on Ebay except it plugs in to your video card instead of the USB. That must have been about 8 years ago.
After looking at ATI's site a bit, it looks like they've altered the function of these All-In-Wonders to really only be one piece of your entertainment system instead of the central piece of your entertainment system (like a receiver for all your connections). It doesn't look like plugging in a PS2 (or any other console) is at the top of their features list.
Your overcomplicating the setup. The easiest way would be to use a diffrent output (There is a PS2 VGA Adaptor that includes 2 channel audio RCA jacks) and connect video directly to your moniter. And as long as your system can handle RCA jacks for audio (theres plently of converters to convert RCA to the mini inputs a PC uses), you can avoid using a capture card.
For my PS3, I use HDMI to my moniter, and Optical to my sound system. No capture device required.