Let me share another scenario where Menu Button becomes critical even though it is not a game.
I have app implement its own tool bars which behave to some extent like ActionBar. Well I did that coz my app was released with 1.5 sdk. At that time there is no such concept. And to accomodate for my toolbars i hide the default title bar. But some of the actions are done through Menu functionality.
Now since in Galaxy Nexus there is no Menu button if you are not using ActionBar and that is hurting me because my app still supports 1.5.
Well there are various work arounds, but none is easy.
That said, the only work around I come up with is to give user all options on my toolbar, so there is no need for Menu at all. I can do this because i only have two actions which are not part of the toolbar.
In your situation, context menu on a button is not a bad soln in a game as game will have only one context in which it is running as compared to having context menu on list items where every item is a different context.
BTW if openOptionsMenu works on ICS and you can ditch HoneyComb after a while (even now the userbase is too low) then try giving both menus based on the version.
EDIT: Well there is another way also to get the MENU s/w button in the below navigation bar. Just set the targetSdkVersion to less than 11. For more details pls read the whole soln.