The reason why she's lost Dorne is that without Yara's fleet there's no reasonable way to get a significant force of Dornishmen north.
They can march north through the Boneway- then they only need to march through the Stormlands, which aren't very mighty after the way, and reach King's Landing. Or, they could march through Prince's Pass and march through the Reach, which is also not much of a threat after the turmoil of the treachery against Olenna.
Of course, all of this is null, because the show doesn't care about logic or geography when it doesn't fit the plot they have in mind.
Riverlands-Robert Arryn
Stormlands-nobody, Gendry at the end of next season
Dorne-nobody I guess....or some Lord from one of the more important secondary houses...lets say, Edric Dayne
There are a couple more things here that are kind of dumb re: the show's handling of those kingdoms:
1) Why is it that when Yara's fleet is sunk by Euron and the Martells are captured, Dany says that she's "lost Dorne"? Wouldn't there still be someone left in charge in Dorne to take over, and why wouldn't they continue to back Dany?
2) Why on Earth were no representatives from these kingdoms (Dorne, Riverlands, Stormlands, Reach, the Vale) invited to the big summit in the finale? Sansa gets invited and sends Brienne, but her invitation makes no sense, since Jon is already there to represent the North. Yet no one from the aforementioned kingdoms is invited to see a zombie for themselves? It seems nonsensical.
1. That's true, but about the "someone left in charge"- I don't think that kind of logic can apply to Dorne. Its lords are basically ignored. I mean, the Sand Snakes murdered the entire Martell line in the dumbest move ever, but no one cared and they just took over Dorne as if all's normal? It's BS.
2. Because the show underestimates its watchers and thinks they can't handle some complexity. Or they're just too lazy to write these kingdoms in and think logically about how they can fit in the plot.