I have to be honest, I had no idea "immersive sim" was even a genre/category. I googled it, and was surprised by the spate of titles that showed up that easily fall into much more specific genres. Wikipedia defined it [roughly] as games with a heavy focus on players' choice affecting the events of the game, but that just feels like a really broad stroke to consider "immersive sim" a helpful descriptor. Like going to the library, asking for a book on cooking, and the librarian sends you off to the "C" section of the entire building.
Many games can be immersive without player choice being a key mechanic, and when I think "sim," I think "simulation" which, for all intents and purposes, almost every game can be considered a simulation insofar as none of them are real, but simulations of events, real or imagined. As compared to say, a military drone pilot; they're effectively "simulating" flying, but they are ACTUALLY bombing war zones. I zoned in your mention of Splinter Cell because it immediately sprung to my mind in as I was researching this genre of game as it does seem they fit the category of game as defined, but I don't see it mentioned or listed anywhere as one (by their definition.)
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