They were, themselves

1. Does "they were, themselves, striking out" mean "Jackson Pollock, Mark Rothko, Barnett Newman, Clifford Styl, or Willem DeKooning were, themselves, striking out"?

2. Is it Greenberg who was the "the champion of an earlier avant-garde"?

3. Does "like all avant-garde gestures" refer to "Latham’s action" meaning" Latham’s action like all other avant-garde gestures..."?

Context:

Greenberg was himself art trained and a painter, and his ideas on art developed in dialogue and personal friendship with many of the major artists of the century whose work he championed. It was their work that provided the exalted exemplars of modern art for postwar artists in Britain and the United States. However, notwithstanding the admiration that many of the sixties artists felt for the work of Jackson Pollock, Mark Rothko, Barnett Newman, Clifford Styl, or Willem DeKooning, they were, themselves, striking out in what appeared to be an altogether different direction. Latham’s alchemical distillation of Greenberg as the champion of an earlier avant-garde, like all avant-garde gestures, marked a difference, a departure, and it did so in the most decisive manner.