Traditionally, you would need splitters (like with the Dazzle), and especially with the Dazzle, you NEED splitters since the preview window is absolutely TERRIBLE with Pinnacle Studios 12 and slightly less terrible with Pinnacle Studios 14. 12 gives you a 1.5 inch x 1.5 preview window that can't be enlarged, lags like all hell even when not recording, and 14 gives you a decent preview window but still lags like all hell. And this is why I use VirtualDub to capture raw video. But with the HD PVR, according to the pictures, there are two sets of component inputs allowing you to use the device as the site of split connection. See reasons above. I'm also not sure if the HD PVR lags while recording like Pinnacle Studios 12/14 do, and if it does, then the only way to play games while recording would be using the TV.
That's how all capture cards work. It would be nice to have it stored onto the card and without the aid of a PC, but then we'd probably run into compatibility issues and standardizations (since no one can ever agree on a standard format) that it would be too much of a hassle at that point.