Individual kings and dynasty have had control over different part of Asia depending over there individual strength. By your inference India which was much more recently under the control of British should be considered a part of England.
Why the areas that make up India should be part of it actually has no common thread. India of today is a union of people who are of
Different Religion, speak different languages are of different ethnicity and are a part of a India not because they always have been one but because British brought them under one umbrella
these people together fought for freedom and thus are united today
When you talk of history you talk of individual kings who ruled areas what is now called India and lastly just because few Indian kings one had influence over Indo-China does not mean it is India by that definition of yours Afghanistan, Cambodia , Indonesia all under different Indian rulers at different point of time should be India and Andaman which was never ruled by any Indian king should not be its part just doesn't add up
Good, patriotic, historically minded Indian people recognize that India's cultural and religious influence has spread far beyond the core areas of the Indus and Ganges valleys.
At the same time they also recognize that many of those regions are, today, outside the bounds of India propr.
That doesn't mean that Thailand was not dominated by Indian thought, commerce and religion before it was taken over by Chinese immigrants.