As the education blogger Whitney Tilson has pointed out, the schools that best represent the reform movement, like the KIPP academies or the Harlem Success schools, put tremendous emphasis on testing. But these schools are also the places where students are most likely to participate in chess and dance. They are the places where they are most likely to read Shakespeare and argue about philosophy and physics.
Without sinking too deeply into this, I'd refer to Caroline Hoxby's New York City Charter Schools Evaluation Project, which Brooks also references. In the section where Hoxby looks at 30 specific polices implemented by NYC charters to see which are associated with achievement effects, the kind of enrichment and curricular policies Brooks refers to were not considered by Hoxby, with the exception of the use of a Core Knowledge curriculum. If the NYC charter community considered these policies to be fundamental to their model, I'm sure Hoxby would have included them in the study. As a whole, they don't.
Various kinds of enrichment do happen in some no excuses charters, but no excuses charters are not defined by enrichment.