This may be long shot and speculative answer.
The Rhoynar are one of the three major ethnic groups from which the
humans of Westeros descend, the others being the Andals and the First
Men. They were a culture of river-faring people who dwelt on the banks
of the immense river Rhoyne in Essos. After being forced to flee in
ten thousand ships during the Rhoynish Wars with Valyria, the
surviving Rhoynar eventually settled in Dorne in southern Westeros.
While most Rhoynar integrated into Dornish society, especially into
the so-called "salty Dornishmen", the orphans of the Greenblood have
retained their Rhoynish heritage and language. The Lord of the
Seven Kingdoms, who sits Iron Throne, claims the title of King of the
Andals, the Rhoynar, and the First Men.
As other answers have explained, the Rhoynar integrated into Dornish society after wars with Valerya, were families like the Targaryens come from.
The reason that information *could matter more to book readers, is because A Dance of Dragons presents Danearys with several prospective husbands/suitors including Hizdahr zo Loraq (whom she marries, but is later imprisoned believed to be a traitor. On the TV series, he's murdered and does not appear as vindictive), Euron Grejoy (who sends his brother Victarion to seek out Dany, but it's possibly a ruse given a few factors), Young Griff (a young man claiming to be a surviving Targaryen, Aegon), and the Prince Frog, whose really Quentyn Martell...
Daario brings the feigned turncloaks to Queen Daenerys in her audience
chamber and presents them as recruits of his Stormcrows. Quentyn and
his friends reveal that they are knights, but ask for privacy in order
to reveal their names. After the court is cleared, Quentyn hands over
his "gift", a parchment containing a secret pact, signed by Ser Willem
Darry and Prince Oberyn Martell, with the Sealord of Braavos
witnessing the signatures. The pact was for Viserys Targaryen to wed
Quenty's sister, Arianne, in return for Dorne's support in helping the
exile regain the Iron Throne. With Viserys having died at Vaes
Dothrak, however, Quentyn now offers himself as a husband for Daenerys
in return for the support of Dorne.
So it may be possible that one reason the Game of Thrones EPs/writers chose to add "Rhoyner" to Dany's dialogue may not just be because Dorne itself wasn't introduced until around this time, but it could of been used as referencing and/or foreshadowing the book & tv events...
Some months later, when Olenna Tyrell accepts an invitation from
Ellaria Sand to Sunspear to discuss the possibilities of an alliance
against Cersei in the wake of the Sept of Baelor's destruction and the
resultant deaths of Margaery, Loras and Mace Tyrell, Varys reveals
himself as the true architect of the alliance, which is in fact to
provide a domestic beachhead for Daenerys's return. When Daenerys
finally sets sail for Westeros she has the combined might of Dorne,
the Reach and most of the Iron Fleet, along with her Unsullied,
Dothraki, and dragons. Varys stands aboard Daenerys's flagship with
her, Tyrion and Missandei, having finally met his new Queen and
pledged his loyalty. With dragons flying in the skies, the second
Targaryen invasion of Westeros is now ready to begin.
Even though they inevitably decided not follow through on in it's entirely, Dany does come to join forces with Dorne, but through Varys instead of the *prospect of Quentyn Martell!