The Layout itself should be landscape.
The Screen has different regions:
First is the board itself (sheet of paper).
On it there is a table (should look somehow handdrawn (see the attachment for the idea, taken from apple keynote) and the different boxes in it should be somehow highlighted for better reading (http://en.wikipedia.org/wiki/File:S…050714.svg)
The numbers below the sheet could be some stones or something like that. This is the design for all action buttons.
The third section is the table with the game stats. Maybe this should be no paper but something else?
The last section is the oponnents board which is a smaller board (it only shows what the oponnent is currently doing)
The Mockup also shows a tabbed pane, Here i have no clue on how to realize that in a "natural" environment. Maybe no tabs at all but just some other stones which then cause the action to switch to another screen.
The main goal (except looking beautiful of course :-)) is readability of the sudoku board itself. If you ever played sudoku yourself maybe you noticed that some color schemes or designs make it difficult to solve the games.
I'm sure that i forget some really important things. Please ask and I try to clarify what I can.