Yes, this sentence is grammatically correct. In this context, "rich" means "varied, interesting, exciting" and "material" means (basically) things that money can buy. Although this reading of "rich" does not necessarily mean "wealthy", a "material life" does imply having enough money to buy nice things. The sentence does not say anything about people in the rest of China.

The sentence is correct. leading doesn't mean 领导，it's just means "they have or are living" rich can mean 有很多钱, but it can also mean 丰富的 material means 消费产品 It's not comparing Beijing to anywhere else. It's just saying people in Beijing have a high standard of living (生活水平很高).