Oscar Wilde is a true Greek and a lover of classical literature, art, architecturel and all forms of Greek art. This serves as an argument in favor of An Ideal Husband and, indeed, most of his work, to be Greek Classical due to his personal preferences. In most Classical literature youwill find the tragic hero, orheroine, a tragica antihero, and a situation solved by no more than Moira (fate) alone. Under this premise, "An Ideal Husband" would satisfy those premises as both male and female characters are drawn to their fates through a situation of which they had no control. That is classical theatre at its best.
However, lest we forget that Oscar Wilde wrote less for form compared to what he wrote for essence. He was upset and highly fed up with Victorian society. He wrote this play as one of several ways of mirroring Victorian society's views of prudence and his own perception of marriage, love, passion, and life. He had somehow to come to a happy medium and created a realistic fictional play with Greek undertones to precipitate an effect that lasts until the 21st century.