What would be the name, government style, main ideology, quality of life and international perception of a restored Beiyang Government as a restored, revived, contemporary, modernized version of the Empire of China founded and lead by Yuan Shikai in 1915 before its dissolution in 1916 sometime before Shikai's death the same year, but with the descendants of the Ming dynasty's reigning imperial family, the Imperial House of Zhu, being enthroned as the restored Empire of China's reigning imperial family instead of Yuan Shikai's descendants formally becoming the Chinese modern day reigning imperial family, ruled by the remnants of the Beiyang Government's Anhui Clique with the remnants of the Anhui Clique's political wing, the Anfu Club effectively controlling most of China's political life with the remnants of the Anhui Clique itself effectively controlling Chinese local government after the PRC in mainland China fell to the 1989 Tianamen Square protests, Nationalist China reconquered the sixteen provinces of Han China excluding Guangdong and Guangxi from Taiwan and the Pengu Islands but were kicked off Taiwan and the Pengu Islands soon after, being confined to the sixteen provinces of Han China before being taken over by the Anhui Clique remnants with help from the Anfu Club remnants and the Ming restorationist, Ming monarchist, adhering to Militant self-defense and tax resistance and traditional Chinese Heterodox folk religion rural secret society and folk religious sect in Northern Han China's Henan, Shandong, Hebei provinces known as the Yellow Sand Society and subsequently transitioning to the restored Empire of China ruled by the Zhu descendants as its reigning imperial family instead of Yuan Shikai's descendants after the putsch by the Anhui Clique remnants and Anfu Club remnants along with the Yellow Sand Society in Nationalist China? Over the weeks, months and years, the Hui Muslims became the dominant economic, political and cultural force in the restored Empire of China, along with being the second largest ethnic group within its territories, mass converting the Han Chinese and Cantonese in Han China and forcing the descendants of the Imperial House of Zhu to publicly renounce traditional Chinese folk religion and reconvert to Sunni Islam, making the restored Empire of China an Islamic Sultanate in all but name with Chinese Buddhism and various aspects of Chinese folk religion being cleverly reinterpreted in order to get the Han Chinese and Cantonese in Han China to convert to Sunni Islam and scholars being sent to Saudi Arabia, Jordan and Qatar to copy and study the political and religious structures of these countries to be reinterpreted in a Chinese, but Hui-influenced and still Islamic context. This gave it the nickname "the Saudi Arabia of East Asia" to both East Asians and Westerners, which isn't helped by the fact that the Ming Sun and Moon Flag, an orange banner with a white circle in the middle representing the moon with another red circle in the far left corner of the white circle in the middle of the Sun and Moon Flag, became the official civil banner and national ensign of the restored Empire of China with the Beiyang Government's five coloured flag, more specifically the initial Empire of China's modified five coloured flag with the five coloured flag's red stripe as a saltire still being reused. 

Like the initial Empire of China created by Yuan Shikai, this restored Empire of China is known as the Republic of China in English but the Empire of China in traditional Chinese, or simply as the actual name of the Ming dynasty, 'the Great Ming State" in Traditional Chinese. The name of the restored Empire of China should be in Traditional Chinese with English romanizations. The Anhui Clique remnants obviously wouldn't call themselves "the Anhui Clique" or the "Anhui Clique remnants" and the Anfu Club remnants wouldn't call themselves "the Anfu Club" or the "Anfu Club remnants", and the restored Beiyang Government obviously wouldn't call itself "the Beiyang Government" so take this in mind when giving them an official Traditional Chinese name.