the key and therefore opening the game menu is emulated with tapping with 2 fingers on the screen.
you can also toggle the textbox/choice list or skip the videos with a two-finger-tap™.
to open the message back-log use either the button top-right while on a map or swipe left during dialogue/choice/input. with swiping up/down you can scroll the log page wise. you close the log by swiping right.