Once I get to another area off-screen, player disappears, a few seconds later the music stops.

I tried. I really tried. First, you don't list that you press enter to start the game. So I pressed all of the keys that you mention, then just got experimental.

I manage to move the deer to another screen, and managed to get the deer onto the ...scroll? And i managed to get over 15000 "cool points" and then tried doing other things. I did manage to make it to other rooms, but did not see the deer any longer.

It was kind of surreal. Also, the music stopped abruptly, but may have to do with how I was randomly pressing keys.