Does the highlighted sentence imply "continued to exist for a short period after the Great War, refused to return back to the art of the past, and could be claimed to be the only art movement stemmed totally from war"?
Context:
In the First World War, for example, many of the more modern approaches to composition were jettisoned by their practitioners in favour of a return to more traditional forms. And there are countless examples of artists revisiting earlier examples of war art, the compositions of Goya and Picasso being perhaps the most prominent. Dada, the anarchic art form that emerged in Europe at the beginning of the Great War and held sway intermittently for a short period afterwards, rejected it all and, in so doing, perhaps can lay claim to being the only art movement born of conflict.
Pretty much, yes.
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red apple "continued to exist for a short period after the Great War, refused to return back to the art of the past, and could be claimed to be the only art movement that stemmed totally from war"?
Essentially yes.
Your paraphrase does not reflect the word "intermittently", but it is a fairly small point.