Chiang Kai-shek was from Jiejiang. Mao Zedong was from Hunan. So why was Beijing dialect (mandarin) kept as official dialect of Chinese for both PRC and ROC (Taiwan)?

Before I try to answer this question, Jiang Jie Shi is not from Zhejiang. In Chinese, when people ask you where you are from they usually ask 你的老家在哪儿？ or 你是哪儿的人？You would answer where your ancestral home is, not where you are born which is more customary in the United States/Canada (not sure about Europe). If you asked him where is he from, he would say Yixing, Jiangsu (because that is his ancestral family home).

Now to answer your question - the Beijing dialect is not the same thing as Standard Mandarin. Standard Mandarin is based off of the Beijing dialect but the two are not the same. The Beijing dialect was the basis of 官话 (guan-hua, literally the speech of the officials known to Westerners as 'mandarins'). The Qing dynasty emperor Yong Zheng basically got tired of not understanding his officials from the deep southern provinces of Fujian/Guangdong and ordered the governors of those provinces to order proper pronunciation for those officials. This was the first imperial decree regarding a standardization of pronunciation. However, the Nanjing dialect was still more prestigious into the 1800s, despite Beijing having been the capital since 1420.

Now when the Republic of China was formed after the fall of the Qing dynasty, the ministry of education convened a conference called the Commission on the Unification of Pronunciation to decide a standard pronunciation of written Chinese characters (this was also the conference where the romanization system of pinyin was adopted and where the proposal for phonetic Latin characters replacing traditional Chinese characters rejected). There were two representatives for each province and one each for overseas Chinese, Tibetans, and Mongols. The delegates were split amongst three groups: Northern Chinese delegates who advocated for pronunciation based on the Beijing dialect, Jiangsu/Zhejiang delegates, and Fujian/Guangdong delegates. Fujian/Guangdong delegates wanted features such as the entering tone that had been lost in most Mandarin dialects but preserved in Min-nan/Yue because it would better reflect Chinese dialects in the deep South. In the end the Beijing dialect advocates won out and Standard Mandarin pronunciation was based off it.

This was before Jiang Jie Shi or Mao Ze Dong were in power. Also you should note that Jiang Jie Shi would be a native Wu speaker and Mao Ze Dong would be a native Xiang speaker (and they both spoke Standard Mandarin with heavy accents from their local dialects), both of which are very different to Standard Mandarin because they are not dialects in the Mandarin language family. Also there are only ~40 million Xiang speakers (mostly in Hunan) and ~80 million Wu speakers (southern Jiangsu and northern Zhejiang) compared to basically all of Northern China, most of Central China, and some of Southwestern China having local dialects in the Mandarin language family.

Also what is 'Standard Mandarin' in Taiwan and the PRC is not exactly the same. Although the touted 'standard' as pronounced by TV news anchors (they are obligated to follow standard pronunciation) from either country are relatively indistinguishable, a lot of native speakers from Taiwan pronounce Standard Mandarin with an accent similar to people from Fujian, as the local Taiwanese dialect is a Min-nan dialect that does not have the retroflex ch- zh- sh-sounds common to Standard Mandarin and many other Mandarin dialects. And since these earlier migrants very heavily outnumber people who came with the KMT to Taiwan after losing the Chinese civil war, the Taiwanese pronunciation of Standard Mandarin is quite easily distinguished from those in the PRC (excepting people from Fujian).

Sources: A History of the Chinese Language by Hongyuan Dong, A History of the National Dialect Movement by Li Jinxi

tl;dr Conference was convened in early days of ROC. Pronunciation of characters was voted on with equal number of votes per province, pronunciation based on the Beijing dialect won out due to the fact that the majority of Chinese provinces speak a Mandarin dialect.