There is absolutely nothing to justify black's king move Ke7. In fact it is a terrible blunder. You can win his queen now:
7 Bg5+ f6 8 Bxf6+ and King must move and you pick up the queen. Your bishop on f6 is protected by your knight.
Maybe there is even a mating attack for white now, I have not looked into it deeply. Maybe if you involve your queen in the attack there is something there.
You must not believe in the computer moves on lower settings. He sometimes will play (very) good moves and then terrible moves like the above.
Generally speaking, moving the king in the opening is rather a mistake than a strong move. There are a handful of opening lines where king moves are accepted theory or necessary but usually they are not.
Can someone tell me why black would choose to move his king here? I'm playing as white against the computer (medium skill level, around 1200) and have seen the computer choose to move the king forward on many occasions playing as both black and white (all games on medium skill level).
Is there something I'm missing that makes this at least a decent move?