TV out doesn't let you display input from a TV source on your computer monitor. It lets you output your computer screen to a TV. If you have TV in on the card as well, you might be able to do it but the image isn't going to be as good.
You can get a VGA switchbox and an adapter for the PS2 to send the signal directly to the monitor. The switchbox lets you just flip a switch or press a button to go from your computer to the PS2 output to the monitor, and the adapter lets you connect the PS2 to the switchbox. Or you could just use the adapter and just unplug the computer from the monitor to play PS2.