In a single PC setup, you are still running OBS and the Game on the same system. All the capture card is doing is taking the HDMI signal, capturing it and inputting it back into the system. This causes the PCI bus to fill with even more data that it was before, and could actually add more strain on an already strained system, possibly causing more lag.
I just built a Ryzen 7 1700x system and was going to use that as my dedicated gaming PC, but did try to use it as a single PC setup for 1 broadcast. "ONE BROADCAST". After that, I just went back to using my previous gaming PC, and now use the Ryzen as a dedicated OBS system.
The issue I ran into with many intensive 3D games was that either the game itself ran like crap but OBS was running fine (HITMAN), or OBS was running like crap and the game was fine (DOOM).