Shaw's plays, referred to as "Shavian plays" are exceptional for their characteristic of contrasting reality with conventional wisdom. In the case of Pygmalion, this contrast is evident in a couple of regards. First, conventional wisdom in England during the Victorian era had it that individuals born into ill-advantaged lifestyles, as Liza the flower girls was, are incapable of attaining anything higher because of inadequate intelligence and under-bred social values. The reality is that intelligence and values are not the limiting factors whereas opportunity and income are. Liza proves in her first few speeches that she has abundant intelligence hidden beneath her heavy dialectical speech and superior values that she does not keep hidden.
Another characteristic of Shavian plays is that they express Shaw's belief in "life force" and that women are attuned to life force in a keener degree than men are. This is charmingly illustrated and expressed in Pygmalion through Mrs. Higgins and Professor Higgins, individually, and through their interactions. This is dramatized by Mrs. Higgins' emotional exclamation while gripping "the table angrily" at the end of Act III, "Oh, men! men!! men!!!", which is prompted by the fact that Professor Higgins has not thought of what Liza's life might become after his experiment is through and callously passes off Mrs. Higgins' and his housekeeper's concerns with, "there's no good bothering now. The thing's done." Plus, their interactions demonstrate Shaw's beliefs by virtue of the fact that she has banished Professor Higgins (her son) from her at home parties because of his inability act in a unified accord with anyone else (except Colonel Perkins as they experiment with Liza ...), thereby frightening her guests.
Another important characteristic of Shavian plays is a didactic, instructing theme. Pygmalion certainly qualifies as a play that instructs. In 1914, the year the play was first performed, lessons about human integrity and dignity were as valid as they were in 1856 when Shaw was born and in 1895 when he became the drama critic for London's Saturday Review. Finally, Pygmalion shines with Shavian wit in the brilliant characterizations and the sparkling dialogue that is true-to-life as well as it is amusing and entertaining.
Your question almost answers itself. One must only look at the definition of "Shavian" which means a play written by or in the same style as George Bernard Shaw. Considering that Pygmalion is actually written by George Bernard Shaw, there is no DOUBT that it is "Shavian" simply due to it's author. However, in regards to style, there must be a reference to some sort of "Shavian eugenics."
You see, Shaw thought that women subconsciously must choose mates in order to have "better" children. Some refer to this idea as the "Life Force" (which I have always found interesting). This certainly fits with Pygmalion. Eliza, being a flower girl, despite her treatment during the play, must choose someone like Higgins or Freddy in order to increase her societal breeding potential (regardless of her thought process). In Pygmalion, in addition to all other Shavian plays, there is acerbic wit involved as well: lots of sarcasm and lots of satire. One of my favorites that fits with the life force is as follows:
HIGGINS: My manners are exactly the same as Colonel Pickering's.
LIZA: That's not true. He treats a flower girl as if she was a duchess.
HIGGINS: And I treat a duchess as if she was a flower girl.
If the reader/watcher of the play reads in between the lines here, we find that it doesn't matter if Eliza marries Higgins, Freddy, or Pickering. They ALL increase her station and the station of her potential children. She MUST choose one of them. Therefore, the sarcasm and satire here show the play to be truly "Shavian."
A Shavian play (i.e. a play by GB Shaw or with the characteristics of writing of GB Shaw) reunites many elements which make them unique: The dialogue is smart, quick, witty, funny, and sharp. The characters are laughable, provincial, bucolic, ridiculous, and do not behave with politeness nor mannerisms expected of the fashionable society. The situation of the story is accentuated by references to the classics, (like Ovid's Metamorphoses as the central plot to the story related in a Shavian way), and using literary techniques that include irony, sarcasm, and puns.
In the main characters, as well as in he character of the phonetic professors, we see all this taking place:
A provincial girl who is paying for lessons to get rid of her cockney accent so that she can sound elegant.
The need to transform her to pretend to be a duchess.
The implication that society would accept anyone who just appears to be rich (ignorant society).
The exaggerated language and the fights between the characters.
All these are the main Shavian characteristics of Pygmalion.
The adjective "Shavian" means "written by or characteristic of the style of George Bernard Shaw," an Irish playwright who lived from 1856 to 1950, primarily in London. It is typical of his work in using humour to make serious arguments about social issues. Much of the comedy revolves around Shaw's debunking of the English class system, and its linguistic snobbery. The concern with language reform and the education of women is also typically Shavian.