"Game Capture" was renamed to "Syphon Client" a few versions ago to be more specific. On Mac, "Game Capture" was accomplished by using a program called SyphonInject to capture games. However, as of Mojave, SyphonInject does not work anymore on Mac. However, OBS still works with other things that can output Syphon video, so the feature remains.
tl;dr There is no game capture on Mac, it's not "missing".