DQN is stateless, so at every point it's reacting to just the current frame (technically, the average of the last 4 frames IIRC) being fed into a CNN and outputing a motion. It doesn't care about ordering all that much because it has no memory. In this case, it's probably learning stuff like 'if there's a key, go towards it' and 'if you have a key, go towards a barrier'. If each screen keeps working the same way, then I guess it would achieve about the same performance as it does now. New screens with new layouts/patterns of enemies will test how well its learned heuristics generalize, though.

Personally, I think that someone should be trying a DQN with an RNN rather than CNN in it to see if that helps on the harder levels. Or better yet, combine it with some of the memory mechanisms and see if it can start doing some real long-term planning.