When in-game texts refer to 'The Kingdom of Argonia', do they mean a kingdom ie a region ruled over by a King (which doesn't fit with anything I've heard about The Hist, Argonians and Argonia save Shadowscales serving the 'royal court') or merely a cheesey stock fantasy descriptor for the landmass?

Secondly, when Shadowscales serve Argonia as assassin and spies - doing what exactly? Argonia doesn't seem to have a coherent state structure and seems intensely tribal bar the Imperial-dominated north. Do these agents oppose the Empire?

1) I think its mostly a generic title. Theres some sort of imperial magistrate 'ruling' over the province, but you are correct in that its not a united nation.
2) Shadowscales are mentioned only briefly in Oblivion, and we're given hardly any information about them. They don't strike me as a native Argonian institution either, so my guess is that its mannish tradition (the imperial dark brotherhood) adapted to local customs.

I'm also going to echo you on the "cheesy stock fantasy" sentiment in regards to all this.

It seems that province of Argonia was divided to "kingdoms" between large cities. According to "The Wolf Queen" there was Argonian priest-king in Lilmoth, and later he was replaced by Magnus Septim, who was referred as King of Lilmoth.
Though, "Kingdom of Argonia" can be reference to some kind of pre-An-Xileel organisation.

It's probably a reference to some Imperial title, similar to how there's a "King of Morrowind", who doesn't have any racial powers.

I mean, most other provinces had existing nobility structures that the Empire simply absorbed. However, Morrowind had a power structure divided between petty kingdoms and the overreaching Great House, pretty much headed by the Tribunal, so it was in their best interests to create a new power structure to exert some local authority rather than relying on the radically pro-Dunmer Great House structure and unpredictable and possibly unstable Tribunal Temple.

I imagine there was something similar to Argonia.

Another theory is that it's the Kingdom of Argonia, and the "monarch" is the Hist.

Their society is impossible to understand, and the King of Argonia is not an Imperial appointment. I never read that anywhere. It's a western, anolytic title for a leadership role impossible to comprehend.

I really hope they make Black Marsh in a game eventually. My guy needs to explore his heritage (he was born in Morrowind).

It'd be hell to give justice to Argonia, but it'd be righteous. Not just Argonians, but toad sages and nedic monoliths/spaceships. Most of the game would take place underwater.