What's interesting about these sketches is that they distort and reflect the humor into something unfamiliar. I think that's what you're laughing at. I don't think you're laughing at the racial stereotype of black people abandoning their parents. I think you're laughing at Jost's embarrassment that comes from him telling racist jokes. And that, of course, flips a very old script. There's a certain amount of genius in writing material in which it's the white guy who is the primary victim of racist material.
Imagine if Greg Gutfield or any of the Fox News funny guys were telling those jokes. They wouldn't be at all funny, even if the comedic delivery is perfect. That's because the jokes aren't funny. At least that's my take.
It doesn't seem like it, but I would put this in the same category of humor as Looney Tunes and some of the Three Stooges. We are laughing because these two guys are doing unexpectedly mean things to each other. You can see this in the contrast between the jokes. Jost's jokes are almost never self-deprecating; he's either made to say racist shit (and unbelievably racist shit) or to mock his wife. Che, by contrast, is typically given jokes that are at his personal expense, like sexual inadequacy. It makes sense when you view it through the lens of playful meanness. Like Looney Tunes.