Is Tianmen in the sentence of Tianmen interrupting the opening of the Chu River the Tianmen City in Hubei Province?

No, Tianmen in Hubei is adjacent to Hanshui River, also called Xiangjiang River, which is a tributary of the Yangtze River.

And this poem originated from Li Bai.

Wangtianmen mountain

Tianmen breaks the Chu River to open clear water and flows eastward to this back.

The green hills on both sides of the strait are against the lonely sails.

This poem describes the scenery of Tianmen Mountain between Anhui County and Wuhu.

Tianmen Mountain, also known as East-West Tianmen Mountain or East-West Emei Mountain, is often called East and West Liangshan Mountain. Liang Dongshan is located in Wuhu City (east of the Yangtze River), and West Liangshan is located in Hexian County (west of the Yangtze River). On the other side of the river, two mountains are chopping with knives and axes, and the cliff is steep, and the water of the Yangtze River flows through it. These two mountains are located in the Yangtze River, the core of tug-of-war in Wu Chu. Since the Spring and Autumn Period, the first naval battle in the history of China-"The Battle of Long Shore in Wu Chu" took place.