I am not to familiar with the procedures at meta and hope this is the right place to formulate a request concerning help with rephrasing a question. The question Is mathematical history written by the victors? was put on hold on grounds of "opinion" and subjectivity. The question presents a historical viewpoint of Boyer, contrasts it with a more recent viewpoint published in a reputable journal, and requests input on this historical issue. Why do the closing editors feel that "answers to this question will [be] based on opinions"? Boyer presents "expert" arguments in favor of his view; similarly, the NAMS article cited presents expert evidence in favor of a "dual continua" view. I don't know if the history of linear algebra is written by "vectors", but the popularity of this tongue-in-cheek comment indicates that some of the opposition to the question may stem from a rejection of the arguments opposing Boyer, rather than issues of "opinion rather than fact". I would appreciate help with rephrasing the question so as to make it fit better with SE guidelines.
The question you asked in the title: "Is mathematical history written by the victors?" is not really answerable. The answer is either a tautological "yes" (by definition, if your version of the history is the one that is accepted, you are a 'victor' in some sense), or non-existent (victory? What game is involved here? How do you win in the game of mathematical history?)
The question you asked in the final sentence: "Have the historians systematically underplayed the importance of the infinitesimal strand in the development of analysis?" is clearly asking for opinions. Importance, after all, is in the eye of the beholder.
The way you formulated your question really is soliciting for debate. What do you expect to get out of this question? An assessment of the number of people who agree with the NAMS article and the number who agree with Boyer? There's no factual question involved as stated.
The only question that I can imagine being buried in your question, and which is appropriate for Math.SE, would be to ask for additional examples from history that supports either Boyer's viewpoint or the NAMS viewpoint. That is, limit the question to facts and not opinions.