In terms of Islamic history, and particularly the empires of India and the Islamic Heartlands in the early modern period, there was a common thread among scholars that they were existing in a 'dark age', and that the 16th and 17th century had been by contrast a 'golden age' for the Ottoman, Mughal, and Safavid empires.
So yes, there was a similar vein of thought that certain periods could be classified as 'dark' and others as 'golden', highlighting differences in how societies viewed their own history. Alongside this we can see the emergence of radical groups such as the Sanusi movement in Libya and Wahhabis in Arabia, who all sought to return to more traditional Islamic values, away from the Sufi orders who they perceived to be heretical. There were other such groups and individuals, such as Jamal Al-Din Al-Afghani, who called for the Islamic empires to switch there modus operandi and operate in the same way that European states were in the 17th century.
This in turn leads me to my second point with regards the perceived nature of 'dark ages' - that they are only perceived due to the contrast with other civilisations that are either geographically or chronologically separate, which are judged to be advancing at a quicker rate. In the case of the Islamic empires, they were contrasting themselves to what they saw as the rapid advancement of the European states, which had quickly and effectively established trading posts on the coasts of India and were pressuring the Ottomans in the Mediterranean. Many contemporaries were aware of the relative decline of their empires from the time of Akbar I, Shah Abbas I, and Suleyman I.
Sources - **Holt, P. M, Ann K. S Lambton, and Bernard Lewis. The Cambridge History Of Islam. Cambridge [England]: University Press, 1970.
Levtzion, Nehemia, and John Obert Voll. Eighteenth-Century Renewal And Reform In Islam. Syracuse, N.Y.: Syracuse University Press, 1987.
Dale, Stephen Frederic. The Muslim Empires Of The Ottomans, Safavids, And Mughals. Cambridge, UK: Cambridge University Press, 2011.**
For the Chinese, I would say more the Warring States Period predating the Qin Dynasty (475 BC - 221 BC) and the long era of division after the Han Dynasty (220 - 581) were seen as dark ages by official Imperial historiography such as that of Sima Qian's, the legendary Han court historian, which was also picked up by many initial Western accounts.
This also mirrors the ideas set by Confucius who looked back to the Golden Age of the Zhou, revised historical classics, and set forth a harmonious system which faulted the chaos of the Warring States Period due to the inappropriateness of unworthy men calling themselves king when there should only be one ruler or Emperor. This attitude is repeated by several waves of court officials and scholars in the Confucian tradition looking back to golden ages. So important was this concept of unity that new emperors would massacre rival households in the same dynasty numbering in the hundreds or thousands; while this practice was deplored on the surface, emperors who were too merciful were often treated unkindly as weak near the tail end of the Han and Tang dynasties especially.
As a result, eras of disunity except for perhaps the romantic Three Kingdoms Era were looked down upon and unification by non-Chinese empires such as the Jin Dynasty (265 - 420) were also marginalized. The Yuan Dynasty (1271-1368) is seen less as a Dark Age perhaps due to deference to Mongol martial prowess which was long respected in Chinese eyes although most rulers after Kublai Khan were seen as mostly ineffectual and losing the founder's Mandate.
In truth, just as the "Dark Age" concept in Europe has been often debunked, the Chinese "Dark Ages" were not only a period of tremendous cultural vibrance but often increased freedoms for the average Chinese citizen. As Victoria Tin-hor Hui notes in The Edinburgh Companion to the History of Democracy, the competition between rulers in the Warring States Period forced them to offer more rights and rewards to those who joined their state as farmers or their military forces allowing people a right of exit (64, 65) from rulers who chose to be too autocratic or stingy.
As for the Islamic empires, I can't say as much but the fall of Baghdad to the Mongols in 1258 is typically considered to be a major event that ended a united Islamic or Arabic caliph with the Ottoman Empire sometimes viewed as the closest regional or religious "heir" although while founded in 1299 did not reach the height of its territory including the taking of Mecca and Medina until the 16th Century.