were are not using the same sense of the word logic here.
when I'm talking about a "logic game" I'm talking about a game that requires the act of inducing the next step.
take for example two classical games:
1) The Memory Game:
http://en.wikipedia.org/wiki/Concentration_%28game%29
2) Mastermind:
http://en.wikipedia.org/wiki/Masterm...8board_game%29
The first is a memory game (hence the name), all you need to finish the game is a good memory and knowing the rules of the game (rules, not logical rules)
The second is a "logic game", in order to finish the game, you must infer from the rows you have played so far which row to place next. so if you had 2 "in-place" balls and 2 "out-of-place" balls, you know that you need to swap two balls, and if in a previous row played you already got a hint to which balls to swap, you can finish the game by act of logical inference.
So while the face-off game has logic to it, in the sense that it isn't completely random, it is not a "logic game".