actually, no. the newer version is called demo because it's a second version/recreation of this game but it's incomplete. because this wasn't written well, the creator decided to recreate it; therefore giving us an incomplete version until they finished it.
however, after a few years, unfortunately the creator isn't interested in this world or it's characters anymore, so they won't be continuing the second version of the game. but, to make up to this, they'll post the rest of the plot in the Liar Liar wiki with the help of a friend, as well as some more information and unanswered questions about the characters.
https://tokimekiwaku.tumblr.com/post/618480560945381376 here's the post where they state this.
i was really sad when i read the post because i've known Liar Liar for a few years now, even before the demo of the second version was released, and i'm once again in the Liar Liar fandom currently. but, hey, at least we'll get to know what the rest of the game was meant to be, as well as more info!