If you can see a storygame on someone's profile, it is on sneak peak. Note that some special characters need to be substituted in when trying to get to the game. In this case, the link is: http://chooseyourstory.com/story/A%20camping%20trip~21%20(gone%20wrong) because the exclamation point is a special character.
This is why it is nice when people give you the link, so you don't have to make it yourself.
Alternatively, last I checked, the site extension will replace the title for sneak preview stories with their links, so that you can just click them as normal.