Nov 16 (Reuters) - Hong Kong shares finished up on Tuesday, as investors embraced positive signs in talks between U.S. President Joe Biden and Chinese leader Xi Jinping. The Hang Seng index rose 1.3%, to 25,713.78, while the China Enterprises Index gained 1.5%, to 9,225.81 points. ** U.S. President Joe Biden and Chinese leader Xi Jinping stressed their responsibility to the world to avoid conflict as the heads of the two top global economies gathered for hours of talks on Monday. ** Investors had expected the summit to help stabilize China-U.S. ties by opening negotiations over the conflicting areas. ** Gaming stocks listed in Hong Kong surged 5.4% as Macau expanded COVID-19 booster shot eligibility, with Sands China Ltd up 6% to become the second biggest percentage gainer on the Hang Seng Index. ** Hang Seng Tech Index, the consumer staples sub-index and the healthcare sub-index gained between 1.7% and 2.6%. ** Mainland property developers listed in Hong Kong added 2.1%. However, shares of Kaisa Prosperity, a property services unit of embattled developer Kaisa Group , tumbled 10.6% after trading resumed a day after the company said its parent’s liquidity issues would not impact operations. (Reporting by the Shanghai Newsroom; editing by Uttaresh.V)