Ok, its a Matyjaszewski paper, so it definitely includes ATRP! I think the Figure 1 you are referring to is kind of misleading, it doesn't differentiate between individual reaction steps, and concepts that are happening within a single pot.
So I think I was essentially right. What they do is make a macroinitiator with ATRP of polyBA, it has a terminal bromine (polyBA-Br). Then they take that purified polymer and put it in an ATRP reaction with divinyl benzene. The divinyl benzene will react a little with itself, and also with the polyBA-Br. This creates a sort of hairy looking star polymer, with some of the vinyls from the divinyl benzene and some ethyl benzene with terminal Brs present because they stop it before full conversion.
The one using the PEGMA (aka PEO methacrylate) macromonomer is simply a monomer that has a polymeric side chain. Its made by esterifying methacrylic acid (or methacryloyl chloride) with OH terminated PEG. Figure 1 bottom half actually has a mistake, they don't use divinyl benzene, they use EDGMA (a bis-methacrylate). This time its just ATRP of a large monomer methacrylate with a bis functional methacrylate. Calling PEGMA a macromonomer is a little cheap, you can buy decent MW PEGMA off the shelf. They should have at least drawn it as a methacrylate, not just a terminal alkene.
The supporting info often contains this kind of nitty gritty, its where I went to figure this out.