You're mixing a couple different points in post...
"Vietnamese girls enjoy their popularity among Chinese man and I'm one of them"
Looking at just the sample sentence, I thought the speaker was one of the Vietnamese girls, who enjoy/like/appreciate the benefits of being popular with Chinese men.
Since we know the speaker is a guy, the meaning of the sentence changes: "...and I'm one of them" tells us that the speaker is one of the Chinese men who like Vietnamese girls.
My question is: This guy here is trying to say that "young Chinese man like Vietnamese girls and so do I" - Am I correct?
No, you're not quite correct. When you say "and so do I," you're implying that you have the same interests as another person or group but you're not actually part of the group. In this case, you might be a Japanese man instead of a Chinese man, or you could even be a Nigerian woman. What you have in common is that you like Vietnamese girls.