Notice the black and white parts conspicuous by their absence
As far as why the left tends to talk about racist structures, there are many reasons, but here are a few:
1. They are wittingly or not influenced by Marx.
2. They tend to see the world in terms of victim and oppressor. Victims are in no way responsible for their condition. The explanation is fully in terms of the oppressor and in particular in terms of an oppressive system.
3. The left tends to be skittish about moral and spiritual conditions and solutions, favoring instead the political. This is in part due to a tendency to deny agency, free will, and moral responsibility.
4. As such they tend to focus (again, due to downstream influence by Marx) on material wealth and well-being. Thus systems such as capitalism tend to be seen as root causes or explanations today rather than moral ones (racist beliefs and attitudes).
What then is a racial structure or system? This is a metaphysical question and, as in most cases metaphysical, there will not be an uncontroversial answer.
But we'll hazard a start.
We might begin by thinking about the structure of a building. The building itself is a structure--an artifact, a human creation. Are buildings racist? Perhaps one built by the Klan to hold Klan meetings, though whether it is racist or not might be contingent on its actual use. (Is a building built by the Klan but turned into a homeless shelter in a black community still a racist structure?) But buildings don't seem to be the sort of structures that the left has in mind when talking about racist structures.
Rather the structures--the artifacts or creations--seem to be certain systems. What is a system? Perhaps we might understand a system in terms of a set of rules (perhaps laws) and practices which humans create and engage in. When a paint crew agrees to divide up how they paint a house, they develop a set of rules (perhaps never explicitly agreed upon) and practices for how best to paint the house ("I'll cut in the corners, you spray and move ladders, etc.")
What systems are racist systems? To answer that we'll need to come to grips with what racism is; I intend to do that in short order in another post, but for now we'll just have to work with our intuitions and provide examples that are at least in the neighborhood. A governmental system can be a racist one if, for example, racists make some of the laws which are intended to treat some racial groups as having less dignity than another without just discrimination as a class and not on a case by case basis. For instance, so-called "Jim Crow laws" which treated blacks wholesale as inferior would fit this description. Of course the Civil Rights movement abolished such laws, so to that extent the legal and judicial system today is a less racist one towards blacks.
So if we're going to talk about racist systems we need to have before us concrete examples of different systems, that is, if we're to identify the racist from non-racist ones and provide solutions for eradicating them. Here the left is often short on specifics. From an epistemic point of view (beyond identifying what racism is) the matter is purely an empirical one. The system the paint crew set up in order to paint houses more efficiently--raising their own profit levels while at the same time lowering the cost of home owners employing them is hardly a racist one. A paint crew that set up a system wherein they charge whites more because they think whites are inferior as whites is a racist one.
Is the educational system racist? Are public schools run by teachers' unions who pay dues to the (leftwing) NEA, racist? It would be odd if most teachers and administrators were (let us reasonably suppose) racists and in fact intend that their policies help those of other races. It would be odd because, as I see it, one could not have a racist system if those making the policies and shaping the practices are not and never were racists. (Of course there could be practices or policies in public schools that are holdovers from previous racists in the system; this again is an empirical matter.) The racism would have to be accidental. Could there be an accidental racist system?
The left seems to think so; or at least they act as if there can be racist systems even if those making the rules, policies, and performing the practices are not racists. (See Eric Holder's infamous prosecution of the Ferguson police department based solely on "disparate impact.") This is because they tend to call a system racist only if the actual outcomes tend to be better for one racial group than another. But as I see it this is either a conceptual confusion or a willful, semantic distortion.
The system in the NBA is such that blacks fair better within the system than Asians. The outcome of the system is such that there are more black players playing and making more money than Asians. But that system as such is not a racist one. For various and sundry reasons blacks tend to fair better in the system. Of course, that's not to say that there is no racism in the system; that will depend on how many Donald Sterlings there are and the extent to which their racism bears on the rules, policies, and practices. The devil is in the details.