The other answers so far give good suggestions for what to call someone who’s an expert in multiple fields of study or professions. But, most of those terms do not apply to athletes, which is what you were specifically asking about. For example, polymath is a great word for this in other contexts, but athletic accomplishments never make someone a polymath. Here, then, are some American English expressions for an athlete with diverse or comprehensive skills.
Someone who has mastered all the skills of a sport is the complete package, or the full or total package. (It always takes the definite article, perhaps because there is only one package comprising all skills, but it’s used as a description of an individual athlete.) This one is slightly informal.
Someone with three distinct skills or roles, as in your example, is a triple threat. This one is also informal, and could be a double, quadruple or multiple threat instead.
A player who excels at both offense and defense is a two-way player.
Someone who plays multiple positions is a two-position or three-position player, and someone who plays multiple sports (which has become rare in America) is a two-sport or three-sport athlete.
Several adjectives that aren’t specific to athletics would apply here, most commonly, versatile.
Some sports have more specific terms for a player who plays multiple positions, with the most common being to put a slash between the positions. For example, a center/forward, which can be pronounced as either “center forward” or “center slash forward.”
Finally, in America, what you call “an all-rounder” is an all-around athlete. This is the most direct equivalent, although slightly more formal.