The speech to the Dothraki is not something random. It has significance.
This takes us back to season 1, episode 7, "You Win or You Die". Wherein Ser Jorah receives a pardon from King Robert Baratheon via a liaison at the local market, but has second thoughts as to his own allegiance. He ends up saving Daenerys Targaryen from being poisoned by a wine merchant who offers her a cask of "a dry red from the Arbor, nectar of the gods" for nothing in return.
Enraged by this, Khal Drogo, Daenerys's husband, then vows in front of the Dothraki riders:
And to my son, the stallion who will mount the world, I will also pledge a gift. I will give him the iron chair that his mother's father sat upon. I will give him Seven Kingdoms. I, Drogo, will do this. I will take my Khalasar west to where the worlds ends and ride wooden horses across the black salt water as no Khal has done before. I will kill the men in iron suits and tear their stone houses. I will rape* their women, take their children as slaves, and bring their broken gods to Vaes Dothrak. This, I vow, I, Drogo, son of Bharbo. I swear before the Mother of Mountains as the stars look down in witness.
Daenerys repeats these lines later in the series, in season 6, episode 4, "Book of the Stranger". After being captured, she is interrogated by the Dothraki khals at the Temple of the Dosh Khaleen:
I know where I am. I have been here before. This is where Dosh Khaleen pronounced my child the Stallion Who Mounts the World. […] This is where Drogo promised to take his khalasar west to where the world ends. To ride wooden horses across the Black Salt Sea as no khal has done before. He promised to kill the men in their iron suits and tear down their stone houses. He swore to me before the Mother of Mountains. […] And here, now, what great matters do the Great Khals discuss? […] You are small men. None of you are fit to lead the Dothraki.
So, ascending the Iron Throne is not only Daenerys's dream based on her claim to it. Her ambition got stronger due to the vows made by her husband in front of the Mother of Mountains. She repeats the same vows once again, only two episodes later, in "Blood of My Blood":
Every khal who ever lived chose three blood riders to fight beside him and guard his way. But I am not a khal. I will not choose three blood riders. I choose you all. I will ask more of you than any khal has ever asked of his khalassar! Will you ride the wooden horses across the black salt sea? Will you kill my enemies in their iron suits and tear down their stone houses? Will you give me the Seven Kingdoms, the gift Khal Drogo promised me before the Mother of Mountains? Are you with me? Now… and always?
That's how she acquires her new khalassar and leads them with her to Westeros.
In her final speech to the Dothraki in King's Landing, Daenerys says:
Blood of my Blood. You kept all promises to me. You killed my enemies in their iron suits. You tore down their stone houses. You gave me the Seven Kingdoms!
So, the speech to the Dothraki was not some random words spoken by Daenerys. All along, she was thinking of killing her enemies and destroying them completely if they get in her way of conquering the Iron Throne.
*Even though this is not Daenerys's motive, Dothraki being Dothraki, they went ahead and misbehaved with the women of King's Landing.