Regular precipitation in terms of snow usually melts in a measured fashion into the rivers of China, southeast Asia, Bangladesh, and eastern India. Well, not exactly regular. India and China are monsoony. I presume that without the glaciers as a freezer, precipitation will fall in the same amounts, but disperse immediately, causing regular flooding throughout these areas.
Bangladesh already experiences horrible regular flooding from some rivers due to rising sea levels coupled with the melts.
Sichuan, just east of Tibet, is an interesting case. Si means four. Chuan means rivers. Sichuan takes four rivers frim Tibet and waters much of China, but not in an entirely natural way. Long ago, a complex system of gates, sluices, and dams was created to distribute the flow more evenly. Terracing the hills also helped tremendously to slow sudden rain and overflows. Travelling by bus through Sichuan during its 100-year flood, I saw some of these things in action.
In the center of Chengdu is the Museum of Science and Technology, with a scaled mockup of the system in a large room–push the button and the flood control system begins.
I dont think the article means 2 billion without water, but rather 2 billion without regular river flow, a slightly different disaster.
What can they do? Maybe build more dams? Some research suggests that the giant Wenchuan Earthquake a few years back was precipitatef by the recent dams built in that area.