I think your question is operating under some misconceptions, about the dominance Latin in the West and about Asian languages.

Yes, Latin is an ancestor language to French, Spanish, Italian, Portuguese, Romanian, and to some extent English (though English isn't a Romance language, it's Germanic). Anyway, the first 5 are all Romance languages (there are other, smaller Romance languages), and are part of the Italic sub-group of Indo-European, a much larger language classification.

Asian languages don't have such a close correlation though. Chinese languages are part of Sino-Tibetan, but unrelated to Japanese and Korean, and whether Japanese and Korean are related to each other or to Mongolian (the Altaic hypothesis) is debated (and generally considered disproved). Then, once you get into South-East Asia you are mostly dealing with whole sets of other language families.

I presume by 'no letters but rather characters' you mean Chinese languages and Japanese. There is some relation here, in that Japanese kanji are derived from Chinese, and that for a long time Chinese writing dominated Korean literary culture. But in a sense the adaptability of the logosyllabic nature of Chinese writing masks the fact that it is possible to write a single 'Chinese' and speak entirely different languages.

So in one sense, yes, Chinese writing lies at the root of literary practice and culture in China/Korea/Japan, but not elsewhere, and not as a root language like Latin in Western Europe.

edit: spelling and opening line.

This may be a question for /r/Asklinguistics, if you don't get an answer here.

I always like to tell people that China is basically what the Roman Empire would look like if it had never fragmented. Thus don't think of China as merely one region in Europe, think of it as analogous to the whole of the Mediterranean.

So with that said, you can consider Sino-Tibetan to be more analogous to Indo-European (broad linguistic family), Old Chinese to be Latin (linguistic root), and the various Chinese "dialects" now to be the equivalent of Romance languages now.

Japanese and Korean are completely different in syntax despite some loans in vocabulary, so that they should not be considered as offshoots of Chinese or Sino-Tibetan. This is kind of akin to English being a germanic language, despite being quite Romance based in vocabulary. It's the essential grammar that matters.

Now with all of this said, I'm wondering if anyone here has a high level of fluency in two or more Chinese dialects as well as two or more Romance languages. I personally feel the intelligibility of Chinese dialects between each other are worse than Romance languages between each other, but that could just be personal bias.