Yes it was, the film captures this accurately. In 1995 the dominant teams in international rugby were New Zealand and the winners of the 1991 world cup, Australia. England and France were rated as the next best. South Africa, by contrast, had only been playing international games for a few years, having been banned during the later years of apartheid. Most commentators saw them as a hard-working and physically strong team, but without the technical brilliance or speed of their main rivals. During the tournament New Zealand emerged as overwhelming favourites, partly but not only due to the impact of winger Jonah Lomu. South Africa's victory in the final really was a major upset, although many of their players went on to have long and illustrious careers.
Rugby union, the sport featured in the film, is a game between two teams of 15 players. The object is to score points either by touching the ball down in the goal area at the end of the pitch (a try, five points plus a possible conversion) or kicking the ball between the posts and over the crossbar (a penalty goal or drop goal, three points, or a conversion following a try, two points). Teams may only advance the ball by running with it or kicking it. Passing forward from the hands is not allowed, unlike (American) football. And also unlike American football, blocking a player who does not have the ball is not allowed, and there is no system of "downs" to guarantee possession to one team or the other (although something vaguely similar does exist in the 13-a-side sport of rugby league). Instead, a player who is tackled must release the ball so both sides can contest possession of it - although if neither side can win the ball the referee will call for a scrum. Rugby union is widely played around the world, most extensively in the UK, Ireland, France, Australia, New Zealand, Argentina, Italy and of course South Africa. In SA it was predominantly played by whites during the apartheid era. Although that is now changing and many of South Africa's current top players are non-white, it explains the hostility to rugby which many of the black characters express in the film.