having one or two christian is not the criteria here, in that case judaism also spread to india, china afghanistan etc, the criteria is having a christian dominant areas and kingdoms. Christianity did spread to axum and ethiopia without roman influence, but largely christianity spread because of roman influence.Not really, Scotland, Ireland, Russia and Scandinavia are not Christianized by the Roman Empire, but by independent Christian churches or by themselves.
In Africa, Egypt and Ethiopia already have many Christians before the Roman legalize Christianity in the Roman Empire.
In Asia, The Middle East, Central Asia, China and Kerala also have interconnected Christian community which couldn't be the result of the Roman Empire spreading it there.
Also how did you get that map? Did it count some Indian sages visiting those areas as sign of those area having Buddhist or Hindu community?
What I remember is that there is an Indian sage who immolate himself in Antioch and that's it.
Christianity do have its fringe area too though like Tibet and Korea. If you want to go further, there are records of a church in Sumatra which predate Islam arriving in Indonesia or the sign of cross beneath an old temple in Japan which would predate Buddhism in Japan, however these would be just a suggestion or coincidence.