I tried the latest build of Construct2, and exported to CocoonJS, but the Save / Load issue is not acting the same as on PC. It appears as if it is trying to work, but all it does is restart the current layout when 'load' is used. :/
It is definitely acting different from how it did last build. I have text on the screen that I print to show what state it is in (like in your tutorial). Before, it would state that there was 'NO SAVE GAME' when I would load, but now it says 'LOADED', which tells me that it thinks that it has loaded the save, even though it really has not.