I don't believe there is much scope for going into detail on this, because Kissinger's assertion not only seems like Orientalist posturing, but is potentially outright wrong. Mao's cadre of officers in the Yan'an Soviet read Clausewitz, rather than Sun Tzu, as their main guide to military strategy during the Second Sino-Japanese War and the renewed Chinese Civil War.

For Mao, Clausewitz's study of warfare, heavily informed by the 'War of Liberation' waged by the German states – and the German people – against Napoleon in 1813-14, was absolutely valuable to his own strategy for fighting Japan, where the problem was really very similar: a culturally-linked people divided across several states (or at least statelike entities as far as the warlord cliques were concerned) trying to resist an outside invading power. The basic thesis of Mao's critical military essay, On Protracted War, is ultimately a Clausewitzian one: it recognises that a guerrilla force can only weaken an enemy so far, and that there must be a confrontation – or at least the threat of one – between concentrated conventional forces in order to reach a decision. As Hans van de Ven has argued, On Protracted War's thesis for the war against Japan would be ported over to the Civil War: the Communists' guerrilla warfare allowed them to not lose the war, but actually winning it meant developing the mechanisms required to transition that army to conventional warfare to challenge the enemy in the field.

Mao's relationship with Sun Tzu remains somewhat of an under-studied one, but the two were never particularly intellectually compatible. During the strategic conference at Zunyi in 1935 where Mao ousted his Soviet-backed rivals within the Party, he had been accused of aping his military thinking from Sun Tzu and the Romance of the Three Kingdoms – in fact, he later admitted to having not even read the former by that point. Some subsequent commentators suggested that Sun Tzu's influence can be read in Mao, but as far as I can tell the most academic of these was a review of a recent translation of Sun Tzu by Scott A. Boorman and Howard L. Boorman in 1964, where the translation by Samuel Griffith cited a grand total of one text from 1936 where Mao cited Sun Tzu for this rather self-evident statement: 'Know your enemy and know yourself, and you can fight a hundred battles with no danger of defeat.' This is not a particularly specific one and to be frank doesn't imply influence so much as a basic currency that Mao drew on. Beyond that, the reviewed work by Griffith's cites a whole two parallels between some of Mao's writings and those of Sun Tzu where Mao might have been consciously echoing bits of Sun Tzu. But some repeated aphorisms don't represent a fundamental intellectual consonance.

Indeed, one thing the Boormans' review notes is that the PLA's main commentator on Sun Tzu, Guo Huaruo, suggested that Mao's military thinking had evolved beyond Sun Tzu's, because the latter was too constrained by his environment. According to Guo, Sun Tzu did not distinguish just or unjust wars because he was part of the 'exploiter' elite class in feudal Chinese society; he preferred quick offensives rather than allowing protracted wars of attrition; and he focussed on the commander at the expense of educating the ordinary soldier. Even the PLA found Mao 'deviating' heavily from Sun Tzu – that is of course on the presumption that he was following Sun Tzu in the first place – and suggesting a strategic outlook much more informed by both Clausewitzian theory and the practical realities of 1930s and 40s China.

Sources and Further Reading

• Hans van de Ven, China at War (2017)

• Francis Miyata & John Nicholson, 'Clausewitzian Principles of Maoist Insurgency', Small Wars Journal, 2020

• Scott A. Boorman, Howard L. Boorman, 'Review: Mao Tse-tung and the Art of War', The Journal of Asian Studies Vol. 24, No. 1 (1964), 129-137

Contrary to /u/EnclavedMicrostate’s claim that Mao only cites Sun Tzu on knowing your enemy, part 3 of Mao’s Strategic Problems of China’s Revolutionary War (中国革命战争的战略问题), written in the December of 1936, directly quotes The Art of War as saying “[avoid] an army when its spirit is keen, but [attack] it when it is sluggish and inclined to return” (Lionel Giles translation, 避其锐气，击其惰归). Mao then names Sun Tzu again in the next paragraph when stressing the importance of deception. (如孙子所谓“示形”之类（示形于东而击于西，即所谓声东击西。）)

The anecdote Hans van de Ven shares on Mao having not read The Art of War when he clashed with Kai Feng at Zunyi is cited from Pantsov and Levine’s Mao biography where Mao is directly quoted as saying “At the time I had only read The Romance of the Three Kingdoms, not The Art of War. […] Afterwards, setting aside other things, I made it my business to read The Art of War.” We have strong reason to believe he did just that, as in a letter penned to Liu Ding and Ye Jianying on October 22nd of the following year on the purchasing of textbooks for teaching military strategy, Mao specifically requests the purchase of The Art of War. And two months later Sun Tzu is directly quoted in Mao’s article referenced in the paragraph above. Coming back to Hans van de Ven’s remarks on Clausewitz’s On War influencing Mao’s On Protracted War the most, the influence of The Art of War on Mao during this time is still noted alongside the likes of Ludendorff’s Der Totale Krieg and the Soviet army’s Field Training Manual.

Another resource supporting The Art of War’s close relationship with the PLA’s strategy, and one that may be of most interest to the OP, is military historian Gary J. Bjorge’s Moving the Enemy. The work places the Huai Hai campaign, in which Mao played a key role, within an Sunzian framework to examine a “Chinese theoretical basis for explaining the decisions PLA commanders made”. In the intro, Bjorge cites the Academy of Military Science’s Tan Yiqing: “If one does not understand what Mao Zedong’s military thought inherited from Sunzi’s The Art of War, it will be impossible to understand its deep grounding in history, and it will also be very hard to explain the unique Chinese characteristics inherent in Mao’s strategy and tactics.” As well as the US army’s Robert B. Rigg, who was stationed in China from 1945 to 1948, in his Red China’s Fighting Hordes: “The impact of Sun Tzu goes beyond his influence on Mao and Mao’s direction of the PLA; it extends down to the combat action and reaction of many generals, and even some of battalion commanders. It provides the spirit, if not the letter of guidance.”

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Sources

Hans van de Ven, China at War (2017)

Alexander V. Pantsov & Steven I. Levine, Mao: The Real Story (2012)

Gary J. Bjorge, Moving the Enemy (2003) [Official download here, No.22]

Mao Zedong, Strategic Problems of China's Revolutionary War (1936.12) [Chinese]

Mao Zedong, Letter to Ye Jianying, Liu Ding (1936.10.22) [Chinese]