I will assume that, by "style," you mean the form/structure of the play. This is a classic Comedy, which means, by definition, that the characters undergo some complications and confusions, but that it ends happily. This happy ending, traditionally, includes at least one marriage, as the plot of a Comedy often involves one or more romantic couples. This sort of Romantic Comedy, ending in a marriage, was the structure or "style" that Shakespeare used for many of his Comedies, As You Like It included.
There are other derivations of plot in traditional Comic structures, some of which also fit As You Like It. Enotes gives a definition that states that a Comedy is "a dramatic performance which pits two societies against each other in an amusing agon or conflict." This is also consistent with one of the main elements at work in As You Like It -- the world of the court versus the world of the Forest of Arden.
For more on Comedies and their structure, please use the links below.