Chinese developed one writing not one language. Chinese dialects are mutually incomprehensible to each other.
Ancient Indians used Sanskrit as their common language along with their own languages.
Ancient Chinese used Classical Chinese as the official language. And dravidian languages are totally unrelated to Sanskrit, unlike Classical Chinese which is the literary written form of ancient Chinese and is related to all Chinese dialects.
Chinese dialects will share far more vocabulary, pronouns and grammar with each other than with Vietnamese, Korean, and Japanese. When writing Chinese dialects and the other languages in characters you can immediately spot the difference.
mandarin: ni hao, wo shi guangdong ren 你好、我是廣東人
cantonese: nei ho, ngoh si gwong dung yan. 你好、我是廣東人
Minnan: lí hó, góa sī Kńg-tang lâng 你好、我是廣東人
hakka: ngi ho, ngai si Kóng tûng ngìn 你好、我是廣東人
vietnamese:Xin chào, Tôi là Người Quảng Đông. 嗔嘲, 晬罗
廣東
Japanese: Konnichiwa, watashi ha kanton jin desu こんにちは, 私は広東人です
Korean: Annyeong, jeonun gwangdung saram imnida 安寧, 저는 廣東 사람 입니다