Never heard of 'spatial presence' before, but if I go by how it's explained (thanx, foxi) I would say that it pretty much boils down to 'having good controls'. If a game has good controls, you pretty much forget you're holding a controller to begin with. You're no longer clicking buttons or moving a mouse, but moving your character through the game world and/or doing the actions available to you without giving it a conscious thought.
Since most modern games manage to do this, it's best to give an example that breaks this. Like Ethan: Meteor hunter (an indie game I recently picked up in a bundle). That game is a platformer, but every so often the running/jumping is interrupted when you have to freeze time and have to stack wooden platform in a different order. Not only does this instantly kill any flow, but the required precision (pixel-like) make it so you have to be more aware of your surroundings than necessary. Which is even worse when you attempt to play it on a game controller.
Immersion is indeed where you identify with whom you're playing rather than as an overseer controlling things (I don't blatantly copy-paste your definitions because simulator games and puzzle games not always have a main protagonist). You buy into the world or concept.
At first, I thought that immersion couldn't be done without having spatial presence (that the latter is a requirement for the former, so to say). But 'Brothers: a tale of two sons' sort of proved that. The controls aren't bad but totally different than you're used to, so most of the game you are aware of the controllers being there. Still...the overall game is so strong that immersion really works.
...but I'm just theorizing here. Does any of this makes sense?
