What's the correlation between an excessive unmarried male population and a big war breaking out?

According to my source below, historically evidence suggests the commentator got it backwards. In some countries and in some wars, (the US WWI, WWII, Korea, Vietnam also Europe in WWI and WWII) wars caused a "small but significant increase in male births". It is documented and there is speculation as to why; but the phenomena is not well understood, nor is it universally true. Other countries, other wars, no such imbalance was created.

Proceedings of the National Academy of Sciences(PNAS) - The United States of America:

Abnormal sex ratios in human populations: Causes and consequences

The finding of a small but significant increase in male births during and after war has been documented in Europe and the U.S. in both the First and Second World Wars (10–12), and in the U.S. for the Korean and Vietnam Wars (13). However, studies of the Balkan Wars (14) and of the Iran–Iraq war (15) did not reproduce these findings. Proposed biological explanations for the observed increase in sex ratio during war include stress to adult males, affecting the viability of XY-bearing vs. XX-bearing sperm; changes in the age structure of the population; and higher frequency of intercourse, leading to conception earlier in the menstrual cycle, all of which have been associated with increased sex ratios in other studies (16–18). Alternatively, evolutionary explanations argue that the increase represents an adaptive equilibrium after the decimation of males during war (13), although critics argue that the increase does not last long enough to compensate for wartime casualties (19, 20). The cause of this alteration in sex ratio at birth during war remains a curiosity.

There are some studies which predict the unprecedented high male ratio imbalance will cause wars, but those studies and predictions are not based on history. The National Academy of Sciences source says the unprecedented low percentages of women is a new phenomena so predictions are highly speculative; but war is one of the predictions. Others include high crime, violent crime and murders.

From the same source as above:

There is also evidence that, when single young men congregate, the potential for more organized aggression is likely to increase substantially (45, 53). Hudson and Den Boer, in their provocative writings on this subject (45, 46), go further, predicting that these men are likely to be attracted to military or military-type organizations, with the potential to be a trigger for large-scale domestic and international violence. With 40% of the world's population living in China and India, the authors argue that the sex imbalance could impact regional and global security, especially because the surrounding countries of Pakistan, Taiwan, Nepal, and Bangladesh also have high sex ratios.

Alternatively: The one child policy has also led to a pretty significant population density imbalance between young people and old people which is expected to have dramatic negative and systemic effect on China's workforce. The economic consequences would tend to put significant negative pressure on China's ability increase or maintain its military budget. This age imbalance is expected to have such dramatic effects that its economic repercussions will be global and dramatic. The source below suggests China's economy is positioned as Japan's before the lost decade which turned into the lost several decades of economic growth.

Source: Brookings Institute: China’s Population Destiny: The Looming Crisis

The "if history is any guide" part is an allusion to mostly alleged famous events. Like The Rape of the Sabine Women or the Trojan War. Not 30 million, just one woman missing is reason for war. Right? Or, just one male too many, if you look from the other side. But investigating this claim as a historian by looking at real events this theory becomes much less convincing.

From a population conservation or population growth perspective, unmarried males are a non problem. Women are the scarce resource here. Being pregnant, giving birth, nursing children takes time, time in which a single male can father dozens of offspring. Unmarried women have seldom caused a reason for concern, the words like spinster are testament to that. But unmarried males are seen as much more aggressive, especially when young, in this case of a hypothesis primarily due to sexual frustration.

But that is the problem of oversimplification. This is not all about sex, but it is about age, and it is indeed about frustration. Frustration stemming from a lack of a promising future perspective, and not just marital bliss, but economical as well. And whether we ask Marx or Clinton: "it's the economy, stupid!"

From a behavioral ecology perspective, all forms of warfare are instances of collective aggression perpetrated predominantly by coalitions of young men. Such coalitions are manifestations of cross-cultural sex differences in aggressive behavior and may be conceptualized as a form of intrasexual competition, occasionally to obtain mates, but more often to acquire resources for the attraction and retention of mates. All societies have young males, yet wars are discrete events that can take place even after long periods of peace. Therefore, an additional factor is needed to explain the episodic nature of the phenomenon. We have proposed (Mesquida and Wiener, 1996) that the most reliable factor in explaining episodes of coalitional aggression is the relative abundance of young males. In this article, we present additional evidence to that effect. The ratio of the number of men ages 15 to 29 years of age versus men 30 and older in a population appears to be associated with the occurrence and severity of conflicts as measured by the number of war casualties.

— Christian G. Mesquida & Neil I. Wiener: "Male Age Composition and Severity of Conflicts", Politics and the Life Sciences, Vol 18, No 2, 1999, pp.181–189. doi

Let's not forget that sexual frustration is rather easily solved by a number of means with varying degrees of historical precedence and current success: prostitution, gay marriage, the internet, and sex-robots. More seriously but less practical one might look to Freud's theory of sublimation.

The real theory behind males waging war is the so called Youth bulge theory, first formulated by Fuller after ideas from Gaston Bouthoul and expanded by Gunnar Heinsohn:

In his theory about the "youth bulge", Heinsohn argues that an excess in especially young adult male population predictably leads to social unrest, war and terrorism, as the "third and fourth sons" that find no prestigious positions in their existing societies rationalize their impetus to compete by religion or political ideology. Heinsohn claims that most historical periods of social unrest lacking external triggers (such as rapid climatic changes or other catastrophic changes of the environment) and most genocides can be readily explained as a result of a built up youth bulge, including European colonialism, 20th century Fascism, and ongoing conflicts such as that in Darfur, The Palestinian uprisings in 1987-1993 and 2000 to present, and terrorism.

This is fully fleshed out in his book:
— Gunnar Heinsohn: "Söhne und Weltmacht. Terror im Aufstieg und Fall der Nationen", Orell Füssli: Zürich, 2006. (Worldcat; Translation of the title: "Sons and World Power. Terror in the Rise and Fall of Nations")

The main problem articulated in this theory is about attainable social status, economic perspectives foreseeably denied to aggressive young males in growing and ageing populations. Any possible sexual frustration is only added on top and plays a very small role. Since the ageing population in the case of china is more of a problem than the continued but slowing growth, this theory would be still applicable. This has not much to do with scarcity of females (Heinsohn writes that "female uteruses dictate the outcome of the next war"), aggressiveness of males ("it's in their nature, testosterone etc."). This is about how the society is organised, economically and socially.

This focus on sex in the question is rooted in structuralist theory. That can be summarised basically: Everything done in a society comes down to a certain the Exchange of women. As bad as Wikipedia does a job in describing that theory, as a frame of reference for analysis this has some merits. As a societal model of inevitability it is flawed.

Economic problems in a system of inheritance laws preferring primogenitur was for a long time solved in German states with the adage: "The first son gets the farm, the second son is sent into the clergy and the third son is sent into war."