On why Master Kong's grave and temples were targeted: Confucianism began as a state-sponsored religion/system of belief during the Han dynasty (202 bce - 220 ce). In its original form, one of the requirements to be accepted as a Confucian scholar was to qualify via taking imperial examination of the Five Classics (of early China).
The other requirement was to participate in rituals honouring Master Kong, namely, visiting his grave and temples. From Religions of China in Practice (1996), p.6:
"Confucianism" is a complex ritual apparatus, an empire-wide network of shrines patronized by government authorities. It depends upon the ability of the government to maintain religious institutions throughout the empire and upon the willingness of state officials to engage regularly in worship."
Activities of Red Guards Against Intellectuals
There are several layers, mainly political, to this question. The missing context are:
- Mao instigated the Cultural Revolution in 1966. In general, the purpose of this movement was to maintain control and preserve his form of communism. Mao's Red Guards were a direct result.
- One of Mao's key adviser which led to the Cultural Revolution was Zhou Yang, a literary theorist. His 1963 report, "The Fighting Task Confronting Workers in Philosophy and the Social Sciences" (pdf), was presented to Mao. In this report, Zhou Yang warned against the potential harm of China's intellectuals:
What the opportunists and revisionists dread and hate most and have therefore tried in every way to revise is the Marxist theory of class struggle, and particularly that of proletarian revolution and the dictatorship of the proletariat.
- It should also be noted that the Communist Party, from its earliest days, have always sought to control and regulate the activities of China's intellectuals. The Yan'am Forum of Literature and Art, led by Mao in 1942, is evidence of this. Merle Goldman's "Literary Dissent in Communist China" (1967) is important and has more on this point.
So, OP's weblink of the 200 Red Guards from Beijing (Jinggang Shan Red Guard Corps of Beijing Normal University) and Qufu (Shandong) desecrating the grave and temples of Master Kong ("Confucius" in Western literature) on 10th November 1966 -- at the beginning of the Cultural Revolution -- is another incident of erasing the memory of China's intellectuals. There should not be anything particularly personal in their attack on the grave and temples of Master Kong/Confucius.
The fact that this group of Red Guards (from Beijing and Qufu) formed the 'Revolutionary Rebel Liaison Station to Annihilate the Kong Family Business' is incidental.