So, on the surface level, the period of "gentlemanly warfare" reigned in Europe from 1648-1789, or perhaps more realistically, from the 1680s to the 1790s.
It is undisputable that gentlemen, that is aristocratic officers, played an important role in warfare during the whole of what the Germans would used to call the Kabinettskriege era: from 1648 (the end of the Thirty Years War) to 1789 (the onset of the French Revolution). As a result of a common aristocratic culture and language, there was a great deal of transnational camaraderie between officers. Austrian, Russian, Prussian, and English officers all spoke and wrote in French, the language of the European elite. Furthermore, since Louis XIV of France created the first modern military in the seventeenth century, specialist military terminology was often in French. Officers frequently transferred between different militaries, and as a result, there was something of a Pan-European military elite, that Christopher Duffy has referred to as "Military Europe."
From the mid-nineteenth to the mid-twentieth, the viewpoint that wars were fought, "in lace" between gentlemen reigned supreme. Historians pointed to Voltaire's famous description of the Battle of Fontenoy, where English and French officers debate the decorum of which side should give the first volley. This relatively ineffectual military system, in the view of the older generation of scholarship, was swept away by the new ideas and military practices of the French Revolution and Napoleon. The trouble is, since the 1970s, historians have increasingly questioned this viewpoint.
Unfortunately, this stereotype is increasingly being challenged in the historiography of this period. Pointing to evidence spanning from common soldiers hatred of the enemy, to the specific targeting of enemy officers by soldiers, to the ferocity with which the Wars of Spanish Succession, Austrian Succession, and Seven Years War were fought, increasingly, modern professional historians are qualifying that this era might not have been so lacey, frilly, and filled with gentlemen officers doffing their hats as we previously assumed. Also, among academic historians, this isn't a terribly new or trendy argument, even: these debates really got raging in the 1980s, and mostly settled by the time I entered graduate school in 2012.
So, in summary**: gentlemen officers and their international common culture did make for a more limited period of warfare, the idea that this was a "gentlemen's war" or "war in lace" that emphasized form exclusively at the expense of function is overdrawn.**
In order to gain a fundamental understanding of the background of this debate, I would highly recommend reading:
John Childs, Armies and Warfare in Europe, 1648-1789 (1979)
Christopher Duffy, Military Experience in the Age of Reason (1987)
John Lynn Giant of the Grand Siècle: The French Army, 1610–1715, (1997)
Erica Charters, Eva Rosenhaft, Hannah Smith, Civilians and War in Europe, 1618-1815 (2012)
Erika Kuijpers and Cornelius van der Haven, Battlefield Emotions: Practices, Experiences, Imaginations (2016)
For specific debates regarding the American Revolution and whether it was a "gentlemanly war", see:
Holger Hoock, Scars of Independence: America's Violent Birth (2017)
T. Cole Jones, Captives of Liberty (2018)
As always, I would be delighted to answer any follow ups you might have!