In the "blind gamer" formulation, wouldn't it come down to distinguishing themes or "fluff"? I mean, if I'm in that situation and the GM says "You're walking down the dark hall when a group of dark-skinned elves appear, holding hand crossbows and wearing spidery clothing; with them is a humanoid with tentacles on its face..." I'm going to think "D&D." If the GM says "The caravan pulled up outside of the tower and out of one of the wagons stepped a garishly dressed magus of the Covenant of Paris, with his ever-present one-eyed companion close by..." I'd think "Ars Magica." If the GM said "The airship descended from the sky in front of the great doors of the underground dwarven kingdom, with tall horned and tusked humanoids leaning over the railings..." I'd think "Earthdawn."
And so on. This may not be the "soul," but different fantasy RPGs have their own distinguishing features, and one need not encounter a single rule or statistic in order to identify them. D&D is chock-full of unique tropes, or at least "D&Dized" versions of classic fantasy tropes. Now in the above example of D&D, the GM could say "roll percentile dice to attack - see, I fooled yah, we're playing Runequest!" But that's just a gimmick, a parlor trick really. Nothing wrong with that, but it doesn't lessen the "D&Dness" of the tropes, it is just a hybrid of the D&D world with another game's system.
In that sense I would say that the soul of game is more so in the world, the fluff, than in the rules (the crunch). There are commonalities across games, but each game forms its own gestalt.