The Last Of The Starks - S8-E4
Character mistake: Gendry gets declared as Lord Gendry Baratheon of Storm's End by Daenerys. But he refers to himself as Gendry Rivers - the surname given to bastards from the Riverlands. Gendry comes from King's Landing, and bastards from there are called Waters, not Rivers. Given that Gendry is not an acknowledged highborn bastard, he should never have had a surname in the first place.
Answer: This is explained more in the book. Khal Drogo and his bloodriders do intend to help Viserys take the throne, however they do things in their own time. This is what causes Viserys's frustration. In the book, Illyrio Mopatis tells Viserys that he has already waited his entire life to claim The Iron Throne and that waiting a few more years isn't that big of a deal. The Dothraki are a nomadic tribe, which is largely why they have no interest in invading and sacking King's Landing. However, since Khal Drogo eventually grows to love Dany, her assassination attempt by the Westerosi compels him to seek revenge.
Phaneron ★