Marge Livingston is the first speaker in the video, you can safely skip the rest.
In “normal” computer programs you have data and the sequence of operations that are performed on that data. You have a collection of locations where the data is stored and you specify the sequence of those operations. Data in a stored-program computer is accessed sequentially and the operations performed are sequential with the output from one step being the input to the next step.
In the brain, data and operations are mixed together. The connection ARE part of that computation. As you indicated, the pipelines of data are all run at the same time. The processing is still sequential, but massively parallel.
Since the brain connections are essentially fixed, data is not accessed and stored, it flows from one processing stage to the next.
The connections are part of the algorithm.
For this reason, I see that understanding the connection scheme is a critical part of understanding the computation.
For the basic computations I have compiled a list of the operations that I can see that the CC is doing here: