Goldberg's thesis is that Black elites are no longer connected to their poorer peers, and thus they tend to greatly overemphasize the existence of racism as a barrier to Black success. Since they're largely insulated from the daily struggles of everyday Blacks, it's easier for them to complain about White racism than to "engage in an honest conversation about the other problems facing black America that have little to nothing to do with white racism."
It's interesting that this argument, on face, seems to be an inversion of how most conservative Whites characterize rich Blacks. Normally, the existence of wealthy Blacks is raised in contradistinction to Blacks who have experienced racism and disadvantage, the argument being that a wealthy Black person, by virtue of his or her wealth, suffers no disadvantage due to their race. Goldberg, by contrast, seems to be arguing the opposite -- only wealthy Blacks really worry about racism, because the bulk of the Black community has bigger fish to fry.
Now, Goldberg's surmising that there is a gap between how wealthier versus poorer Blacks think about racism is unsupported by any evidence -- unsurprising, since the data we have indicates that there is no significant class divide in how Blacks rate the prevalence of racial discrimination. And as Jamelle Bouie points out, the entire premise of Goldberg's class disconnect hypothesis is demonstrative of Goldberg's lack of knowledge of the Black community.
Here’s the deal: one result of Jim Crow and its economic disenfranchisement is that the black middle class is a relatively recent event in American history. The same is true of the black elite class, which is—and has always been—quite small.
The byproduct of this is that the temporal distance from working-class life to prosperity is fairly short for many black Americans. So short, in fact, that black elites were often the first in their families to obtain a college degree. On a day-to-day level, what this means is that affluent black families share close connections to lower class African Americans—they are parents, grandparents, cousins, or even sibilings. This simply isn’t as true of affluent white families.
Wealthy Black families are far more likely than their affluent White peers to be well-connected to the thoughts and life goings-on of their poorer brethren. It's unclear why Goldberg doesn't recognize this, except for the obvious answer that Goldberg doesn't actually know anything about this topic and yet feels free to pontificate about it anyway. Which isn't, you know, a departure for him or anything, but still.
* I suppose the right answer is, "because it's not like there's another subject he's more credible on". Why should the lack of knowledge stop him now?