This is a very good question, because in all comedy there is a degree of commentary on some aspect of life.
"Comedy of Manners" is defined as: "a comedy that satirizes behavior in a particular social group, especially the upper classes."
As can be seen from the above definition, in order for a writing to qualify as a comedy of manners there must be an element of satire involved. This calls for another definition.
"Satire": "the use of humor, irony, exaggeration, or ridicule to expose and criticize people's stupidity or vices, particularly in the context of contemporary politics and other topical issues."
In "The Conscious Lovers" the satire is directed at the ridiculous habits of the rich in seeking to marry off their children to "the right" person. And by "right" is meant one who fits the parents' agenda and includes no consideration for the desires or wishes of the parties to be married.
Not only is this the case in the work at hand, but the writings of Oscar Wilde especially would fall into this category, as well as many of the works of Shakespeare.