He puts forth a convincing argument that all of the characters are represented in the game and, the world itself is very similar to that of the Sky Island novel in it's segregation and problems. I'll list the characters he outlines here because I actually want to make a few changes:
Dorothy: Booker DeWitt
The Ruby Slippers: The Lutece twins
Glinda the good witch: Elizabeth/Anna
The Wicked Witch of the East: Lady Comstock
The Wicked Witch of the West: Daisy Fitzroy
The Wizard: Father Zachary Hale Comstock
The Scarecrow: First Zealot of the Fraternal Order of the Raven
The Tin Man: Cornelius Slate
The Lion: Jeremiah Fink
The Munchkins: The upper class populace of Columbia
First off, I think you really need to think of the imagery, introduction and roles of the characters and I think this is where Alec gets it a bit wrong. I think it's safe to say that Glinda is actually the Lutece twins and I come to this conclusion from the representation and entrances of Glinda from the movie version.
They greet you when you enter the world of Infinite, and come and go as they please as does Glinda - all the while providing cryptic assessments and helpful statements without really interfering with the natural course of events too much. They take you to the lighthouse which is the representation of the tornado in all Bioshock games (as alluded to near the end of the game): that force which transports the protagonist to their new fantasy land. However, they don't make you get in the chair or perform the tasks to get there: they only start you on the journey.
They interact similarly with Elizabeth and when meeting her to give her the choker they appear to be repeatedly asking: "Are you a good witch or a bad witch?". Do you lose or retain control?
If you watch the Wizard of Oz scene in total you see that Dorothy says that "I'm not a witch at all! Witches are old and ugly..." (around 1:27 in the clip). In the game you see that one version of Elizabeth, the old version, is the witch. She is evil compared to her younger self, though she wishes to change all that and have her younger, pre-witch self saved from the same fate. Just as Dorothy's adventure in Oz prevents her from running away from home and bringing her to the realisation of how selfish she is...
|Old? Check. Ugly? Well, if I'm being unkind...|
This, of course, means that Elizabeth is Dorothy and that Booker is Toto. Booker being Toto is one of the central aspects of the theory because he is always following Elizabeth: often when you're running along, Elizabeth will get in front of you and there's no way to catch her. She also leads you around between worlds and she is the reason that he is in this whole adventure in the first place. He is the faithful follower, dutifully going wherever Elizabeth does and endeavouring to protect her - even if, in reality, she is the more powerful of the duo.
You can see the parallels (or perhaps, more accurately, I see the parallels! :) ) in this clip from the film. The Wicked Witch of the West captures Dorothy and wants the slippers. She takes away Toto and Dorothy pleads for his safety. Toto escapes but Dorothy is left to have her magical slippers stripped from her through her death when the hourglass runs out.
This is reflected in the scene where Elizabeth tells Songbird to leave Booker alone and she goes along with him to the place where she will "die", have her powers removed and be reborn as the future destroyer.
Similarly, Dorothy wakes up in bed at the end of the film - as does Anna/Elizabeth after wishing to be home and for the nightmare to be over. She had left home (though in the game, she was given away by Booker) but was now there again. This also means that the slippers are Elizabeth's reality-bending powers and that, once home, they disappear along with the magic that they brought.
The easiest reference is the Songbird who is a "winged monkey" - sent to take Dorothy/Elizabeth to the witch's tower where she will be imprisoned and lose all hope/be killed.
The problem then is that who are the wicked witches?
Surprisingly it might be Fink and Slate. One of the big things about The Wizard of Oz is that the land was ruled by the Wizard and his daughter Witches (if Oz the Great and Powerful is true to the books!). The Wizard was murdered and the family fell apart.
Well, in Infinite, the Wizard is dying due to being "poisoned" accidentally by the Lutece twins. The organisation that helped found the city, Comstock, Lutece, Slate and Fink are falling apart in disagreements and treachery. Slate has renounced his affiliation with Comstock and has rebelled, questioning the validity of his superior. We also find him, finally, "crushed" by his actions and fight, sprawled on the floor in a pose reminiscent of the Wicked Witch of the East in the film.
|No house though... maybe it floated away?|
I guess the real answer to all of this is that it's all just a coincidence. There is stereotypical imagery used in this game, imagery that just happens to be similar to that found in The Wizard of Oz... but I doubt there is any real inspiration for one from the other. This is, in my opinion, one of the facets of a strong and interesting story - that parallels, discussion and analysis can be drawn out of the work. It makes the story live on and not just become discarded as some throwaway piece of media consumption.
While Bioshock might be the more coherent game, Infinite shoots higher and may well be remembered more clearly.