There's no point using a capture card on a single PC. The only possible use is to capture the entire screen when circumstances don't allow otherwise (eg capturing a game which is highly incompatible with hooks)
Single PC with game capture:
GPU Output -> GPU -> GPU Render -> System Memory -> Encode -> Stream
Single PC with capture card:
GPU Output -> Capture Card -> PCI Bus -> System Memory -> GPU -> GPU Render -> System Memory -> Encode -> Stream
Dual PC with capture card:
PC1 (Gaming): GPU Output -> Capture Card
PC2 (Encoding): PCI Bus -> System Memory -> GPU -> GPU Render -> System Memory -> Encode -> Stream
As you can see, with the dual PC setup, you offload a lot of the work onto the 2nd PC, so it provides a large CPU reduction on the PC you're gaming on. This is the only situation in which a capture card makes sense for PC games.