Laurie Taylor, a PhD student at the University of Florida, discussed two kinds of play spaces in video games: smooth and striated. (She was drawing her definition from theory, but I came in late and didn't catch whose.) In striated space, every subsection of space and game pieces has meaning, as in chess. In smooth space, meanwhile, only specific points have meaning, and the path one takes between them is not important. She made it clear that both kinds of space could conceivably be found in one game, and cited Civilization as a game which includes both kinds of space. Different games may give space meaning in different ways; for example, she said, in a multiplayer game a space may be given its meaning by the community engaged in play or by the puzzle-solving or fighting which goes on there.

Implications? I dunno, haven't thought about them yet, but this is one axis of the dimensions of game space to consider, and vocabulary to describe it.