Does immersion require a rich, detailed story? No! In fact, the opposite may be much better.
Does your average game of capture the flag in Warsong Gulch feel much like a war? Not to me. But why not? Surely we could see how two competing factions might stage some sort of tournaments to keep the other side defeated even if they cannot have open war. Right there, do you see it? I'm having to overthink it. That's bad. The problem is that there is too much lore, too much story. We know too much and from that too much information we can easily determine that Warsong Gulch makes no sense at all.
Team Fortress 2 doesn't mess around with all that nonsense. They just went for the simple point: two mercenary armies of coincidentally equal size, power, and technology, have been hired to do battle on behalf of a pair of greedy brothers. It's set in a silly world which embraces the absurdity of this sort of highly-staged combat.
Embracing the ridiculousness and making that the story gives tremendous wiggle-room when worrying about breaking immersion. Why is there an omniscient announcer at every battle? Why? We don't know! But of course she's there, how could she possibly not be? It just makes sense. Why does it make sense? Because there are no logical or story structures which would contradict the idea of the announcer. So of course she's there. We'd be surprised if she wasn't!
Valve doesn't try to create a deep, story-filled world rich in history to discover. Instead they create a silly world where we feel silly. The silliness is consistent. This works well with their item shop which mostly sells extremely silly-looking hats. While in a fantasy game you may be turned off by money buying a flashing-looking and otherwise inaccessible sword, when everything is silly, someone spending money on a silly hat only adds to the sense of immersion. Immersion in silliness.
This is alternative immersion. This is a different sort of world. A world where flamethrowers are doused with jars of pee, where spies escape notice with a simple paper mask, and where gigantic Russian men fire guns that cost $400,000 to fire for twelve seconds. And it all makes sense, in its own special way.