I don't interpret that like this. You play as state which has a series of rulers, but they are more fleshed out than in games like EU4 and there is more incorporation of personalist politics.
There isn't much to interpret to be honest, because it is not a matter of opinion.
In CK you have relationships with individual people and everything is very personal, from marriages to wars. In Europa Universalis you play literally as a state and your rulers are just a bunch of stats. In Imperator you play as a state (like in Europa Universalis), but you also have some fleshed out individuals who can play a role in the government so there can be a clash of personalities.
So I disagree that it is just a "marketing gimmick". While CK3 has a lot of flaws, it is very distinct in its approach to gameplay.
I am referring to CK2. CK3's interface is too infuriating so I am not playing that. At the same time, it seems to be improving. For example, I heard that one of the DLCs actually adds the economic map mode which was bizarrely missing. Perhaps with time they will return to the functionality of the older games, so I'll just wait a few more years until it is all fixed.
It is very much a matter of opinion. If it were to be a personal simulator, it would be a disastrous game as this element is very shallow and peripheral to success, and the grand strategy genre is a poor fit for it. The CYOA genre like Sir Brante, Suzerain, perhaps King of Dragon Pass is a good fit. This is like saying you are playing individual colonists in Rimworld rather than playing a colony.
Ideally, all of their games should simply have well fleshed out elements which include persons, population, province development beyond the basics, and a decent research system (something like HoI4 or better). Victoria 2 probably approaches it all best, but CK2 is not far behind in terms of detail as there are many ways in which you can affect the domain. E.g., an interesting choice is whether to concentrate your holdings in one county for the bonuses from councilors or go wide. It's interesting to manage the kingdom, come up with bureaucratic solutions like creating a theocratic vassal that would expand on his own. The "personal politics" mostly boils down to pop-up events that repeat over and over.