Tried it on a Touchscreen device now...
That opens a new can of worms:
Opening the menu is almost impossible there, as touch does not generate the mouse events for position the same way a real mouse does, so getting the menu to show up is a game of luck. And when getting it open none of the items could be selected with touch (might be the same problem with the inactive window).
Maybe adding a context menu or a symbol for the info area would be a solution for that.