The Rivals is one of the earliest examples of theatrical pieces that break with the traditions of its time in that it is not created for the purpose of honoring history, nor teach a morale.
Contrarily, Sheridan uses his play to mock and satirize people who would otherwise be considered respectful and virtuous. He also adds irony to the plot by loading it with witty sayings, epigrams, and strange phrases that cause the public to laugh. These qualities are what make The Rivals a comedy of manners: It intends to cause laughter by mocking the serious aspects of society.
In addition to the style, we also find Sheridan's humor in the selection of the names for his characters, for example, Lydia Languish, the ever-dramatic woman in love with love, Captain Jack and Sir Anthony Absolute, Mrs. Malaprop, and Sir Lucius O'Trigger.
As far as the plot itself, The Rivals also shows the common characteristics of the comedy of manners in that it will include the themes of courtship, marriage, love, relationships, and the tricks people are willing to play to obtain what they want.
However, it is the character of Mrs. Malaprop that really drives the comedic nature of the play in that Sheridan puts extremely smart and intelligent-sounding words and phrases, and all are used incorrectly or out of context. This is what starts the coinage of the word "malapropism".
Concisely, the use of satire to mock typical social constructs and the addition of trivial expressions, and exaggerated mannerisms make up for what is typically described as a comedy of manners.