It’s not until several minutes after Danai Gurira’s entrance in the Public Theater’s new production of “Richard III” — the first entry in this summer’s outdoor Shakespeare in the Park series — that you realize how physically different her titular tyrant will be from those presented by other actors.

Yes, Ms. Gurira is female and Black, but neither of those factors should seem particularly surprising, given the exponential rate at which diversity in casting has picked up in recent years. What’s most striking about this Richard is the extraordinary grace and poise. Investing the character with perfect posture and the powerful, fluid movements of a dancer, Ms. Gurira offers a sharp contrast to the “rudely stamp’d” hunchback that Shakespeare presented in a portrait marked by other historical inaccuracies, likely motivated by the politics of his day.

In fact, since the real Richard’s remains were discovered a decade ago, it has been determined that the king was not as severely deformed as legend, propelled largely by this play, had it. Yet I doubt this was an element in Ms. Gurira’s choices, or those of her director, Robert O’Hara. In a recent interview, Mr. O’Hara evoked the crippling effect of bigotry, explaining that his Richard would be ravaged from within.

“Richard hates himself,” the director, whose previous credits include “Slave Play,” told Variety. “And he is acting in the way that people who hate themselves do. If there is a deformity, it’s his interior self.”

On the surface, neither race nor gender figure prominently in Mr. O’Hara’s briskly entertaining production. The cast is racially eclectic, and Ms. Gurira’s Richard is male, albeit seductively androgynous. Costumed by Dede Ayite in a gold-vested black blouse and leather boots, the actress — known to film and television fans for her roles in “Black Panther” and “The Walking Dead” — is lithe and strapping, exuding a feline ferocity and sexual confidence that hardly suggest self-loathing.

Mr. O’Hara is actually less effective at showing us how evil can be internalized than he is at emphasizing inner strength and virtue, by casting disabled actors as more noble characters. Gregg Mozgala, who has cerebral palsy, plays both Richard’s brother Henry IV and the Earl of Richmond, who finally ends Richard’s killing spree and succeeds him as king. Mr. Mozgala’s slight limp doesn’t detract from his dignified bearing, any more than the deaf actress Monique Holt’s reliance on sign language — used at various points in this staging — makes the Duchess of York’s despair over losing other family members, in part to her son Richard’s bloodthirsty ambition, ring less loudly.

The contempt that Ms. Holt’s silent but animated duchess shows for her scheming, morally bankrupt son is, in fact, the closest thing to ill will that Ms. Gurira’s villain/protagonist has to contend with here — and certainly, no one could blame this mother for not loving her child, any more than one could blame the other characters who are seduced by him, in one manner or another, before turning against him.

These include, of course, Lady Anne, who is successfully wooed by Richard after he does away with her husband (and his brother) and father-in-law. Ali Stroker, maneuvering her wheelchair with a frisky defiance, plays pouty princess to Ms. Gurira’s charismatic viper, and a spry comic rapport develops between the two — even as Anne is accusing Richard of murder, and he is inviting her (disingenuously) to content herself by killing him.

Mr. O’Hara generally mines the humor in this dark material, in fact, instilling a sense of wry wit and whimsy not unlike the one he applied to the less bloody but equally provocative and often troubling proceedings in “Slave Play.” He has a potent ally in Ms. Gurira, who can be as amusing as she is terrifying here. When this Richard, trying to win favor with Queen Elizabeth — played by a feisty Heather Alicia Simms — after having her young sons assassinated, says that “what is done cannot be now amended,” you’ll be forgiven for having a chuckle.

Other standouts include Sanjit de Silva, underlining the ham in Buckingham, winningly, as a duke who remains Richard’s ally for too long, and Sharon Washington, who brings a more sobering majesty to Queen Margaret, whose husband and son are among his earlier victims. Scenic designer Myung Hee Cho adds to the simultaneously playful and creepy vibe with a stark set dominated by looming arches that sporadically are lit up with neon (by Alex Jainchill) and revolve around the stage, carrying tortured souls like some sort of haunted merry-go-round.

It’s a fun ride, particularly if you’re looking to escape the present-day horrors for a while.