There is no such sport as 'Rugby' which is merely a style of football, there are two distinct sports called 'Rugby Union' and 'Rugby League', which whilst they have a common heritage and some common skills, are very different in many ways, have different clubs, national teams, laws and governing bodies etc. They have been separate sports for nearly 120 years.
Most people who talk about Rugby are actually talking about Rugby Union, but it would be presumptive to have Rugby as a synonym for Rugby Union, as League is a popular sport in many countries, particularly Australia, where it is more popular than the other.
I do think that most of the questions tagged Rugby so far could be retagged as Rugby Union, and a separate Rugby League tag could be made.