Perhaps the distinction can be made not between Indian and other religions, but between religion and dharma. They have similar meanings, but they are not the same. Dharma is one of those terms that actually has no direct counterpart in English, but it does have at least some connotations which are quite different to 'religion', such as
Emphasis on experiential learning
Emphasis on meditation and self-knowledge
No single representative or definitive single holy text
Inclusive rather than exclusive
And so on. It is quite true that there has been sectarian bloodshed and rivalry in Eastern religions, do you don't want to gild the lily, but this distinction between religion and dharma is still worth bearing in mind.
You've given a very nice modern Western definition of "Buddhist Dharma", but one that doesn't really match up with the usage and understanding of the term in (some) other so-called "Dharmic religions".
In orthodox Vedic Brahmanism, "dharma" (including "svadharma") does have a very similar meaning to religion in possibly most cases.
Moreover, there is not much of an emphasis on "experiential learning", "meditation and self-knowledge". "Knowledge" is "vidya", and it comes from the "veda", Rg, Yajur, Saman and Artharva; and maybe the Vedanta commentaries, the early Upanisads. (See next point how that knowledge comes.) Svadharma is one's duty, and that depends on one's caste. To do this duty is to be in accord with Dharma, ie. religious, or we could say "righteous" (except for the fact that one's svadharma may involve killing or violence if one was a ksatriya, for instance).
Furthermore, the Vedas are very much the representative and definitive holy texts (though not singular), indeed, the Vedas are considered the only real things worth knowing, and they are known by strict memorization which is part of brahmacarya training of young brahmin boys. In addition to this memorization, teachers will also know the grammar and so forth behind it, all still wrote learning.
Also, it is exclusive - only male brahmins can study and practice these things, though any "twice born" men can participate in the yajnas themselves (but only as patrons, not as officiants). Women, lower castes, and people such as those sramanas "who are the scum born from Brahma's feet" are not welcome at all. These lower castes fulfill their svadharma by serving the brahmins, and that is as good as they can get, simply because they are not brahmins (ie. do not have seven generations on maternal and paternal sides that are also pure brahmin).
Just for fun, I decided to check a Hindi-English dictionary (http://dict.hinkhoj.com/
), so see what that would say. Putting in "religion", I got:
RELIGION<===> धर्म (pr. \\dharm\\ )[Noun]
उदाहरण: भारत मेँ अलग अलग धर्म के लोग रहते हैँ।
Example: Religion teaches us to live and let others live.
And for "spiritual", I got:
SPIRITUAL<===> धार्मिक (pr. \\dharmik\\ )[Noun]