They are - just another sub category in 'vegetarian'. Its just a choice that they have made that they would like to consume eggs but not meat. There are certain communities in the coastal regions of India, who consider themselves as vegetarian but still eat fish - fish is vegetarian for them.

The point is that when it comes to vegetarians, assume they don't consume any meat, fish, and eggs; don't just blindly push eggs onto them.

As to your point about the people in the Indian subcontinent being in minority as to what vegetarianism means to people, do keep in mind that the origins of vegetarianism lie in India.
http://en.wikipedia.org/wiki/History_of_vegetarianism