it doesnt disappear because i have mine set up right now like that. So something on your end of things, probably clicked hide on it. You're suppose to be the "Game Capture HD60 Pro #1" because thats the one made for your capture card. I had my suspicions when you posted the pics of your settings because the the pro goes into a PCI slot, so no latency. The Elgato Capture HD was the software made for the original Elgato HD, so older and slower and can't handle nearly as much. So yes, you're gonna want that as your video capture.
If you want you can try and see if thats the only thing you need to change before you do anything else as far as audio settings and what not, because maybe that is all you need to do since you PC can handle it no problem. Let me know