You can perhaps design a game that is difficult to solve by AI (though I wouldn't bet on it). The question with AI is usually not what it can't do but what it _can_ do. If a certain system fails at your task but performs well in a range of other tasks that are considered useful and challenging, then it's worth consideration. Especially so if there is no system that can perform well on that one task.
The way you'd train a neural network with that footage is comparing the recording of the neural network playing the game to the recording of the speedrunner, and scoring it based on the difference in the footage.
However it wouldn't really be learning "from scratch" and "end-to-end" anymore, since you're essentially teaching it to imitate and play like a human player. Also your network would likely be just blindly executing a series of learned actions, without any real understanding of the game. If you confronted it from some situation that's not part of some speedrun it memorized, it would probably be at a loss. Pretty useless.
In the example above, at no point the neural network would be watching the video footage. The reference footage is just used for (automatically) scoring how well it does during training. It's not fed into the network itself in any shape or form.
Setting up a stupid method of getting to the goal doesn't disqualify said goal.
That's not a very useful goal. I can trivially make a game that is impossible for such an AI to win. It would require you to enter a 1024 bit code [0] and if you are correct you win. For a speed runner the time it takes to beat the game is merely limited by their typing speed because the code is always the same but an AI with no prior knowledge can only brute force the solution. How does the speed runner win in the first place? They ask the game developer and then post the code on a wiki.
[0] an euphemism for minecrafts crafting system