you should compare it with a game whose rules you don't know, being able only to understand your score. like trying to play spider solitaire on windows without knowing how the game works (it allows you to undo your moves).
notice that in your example of solitaire, knowing the values of hidden cards really changes the nature of the game and makes playing the game much less strategic
It is clearly an April Fool's hack.
This is from the paper. "I tried again, and it was a huge breakthrough: Mario jumped up to get all the coins, and then almost immediately jumped back down to continue the level! On his first try he beat 1-2 and then immediately jumped in the pit at the beginning of 1-3 just as I was starting to feel suuuuuper smart (Figure 7). On a scale of OMFG to WTFLOL I was like whaaaaaaat?"
I do agree with you though.
This is why he mentions that Karate Kid didn't work well, because one of the factors of a successful play-through was that your opponents health is decreasing, which is something that this AI doesn't look for.
The ability to rewind time wouldn't make for a very interesting play-through of Battleship, but depending on how game state is stored, it might not even be able to accurately deduce a good game state from a bad one.
I don't believe that was the case. From the video he mentioned it using the power kicks up all on the first enemy because they produced the most favorable outcome for that game, at the expense of later games when more powerful moves are needed (since the AI can't plan that far ahead).
I can't watch the video at the moment but I imagine the paper goes much farther in-depth with the internals of this AI.