Setups like this with Qe2 and 0-0-0 are fun to play. I've done it before and then launched a big attack.
But no matter how fun a setup looks, your opponent gets to make moves too 
So you have to weigh the positives and the negatives.
9...d5 with 10...c5 and 11...d4 (as suggested by the engine) mean black's pawn storm is coming a lot faster. Also this obviously claims more space and seals your b2 bishop. After 9.0-0 you can still attack his king, but your king is safer, and black has to live with his small center (no d5 for black).
But even without the engine's d5-c5-d4 push, lets imagine black plays 9...Nbd7 10.0-0-0 Nc5. Both player's attacks will take many moves before a real threat on the king is made. Looking at this imagined position, IMO there's nothing special here that should compel white to go for Qe2 and 0-0-0.
My two cents.
Short version, ninth and tenth moves seem to be weak, but I'd like to hear from people why. I move my queen up to set up a castle, and I then castle the following move. The initial move is deemed a weakness by a basic computer glance, and the castle further so, implying that entire thought process had a flaw I overlooked. For the rest of the game I was comfortably safe or in control, with an early scoop before they saw if I could finish them using the superior position I had acquired.
For my ninth move, I see my queen is now close to being pinned to my king by their rook, the column is lined that way but the pawn is in the way. If they could break it, they could punish me, but I did not see their way to do so. My opponent tried to rush this, but by move 10 they had lost their chance even as they attacked that pawn for all it was worth.
When I set the position up vs the highest level computer they offered in finish vs computer they chose pawn to c5 to attack my knight instead on their move 10. I see some merits to the attack, but I don't think I see them all and I don't think exploring the computer's variations will cover it, certain concepts I don't think about seem likely at play. I'm not one to say what the computer says is the word of god, but it obviously sees more than a player of my caliber, so I'm going to give it credit for that. I used it to find moves to take a closer look at in situations where I might not have given it a second thought, and I tried to spot the clear edge myself, but I think this is a case where the input of others is going to be more valuable.
So anyways, do you agree that my 9th and 10th moves had problems, and if so, is the computer's suggestion a good way to punish that weakness. If not, what would a better punishment be? For my own gameplay, what might have been better moves than what I did for 9 and 10? If you see anything else worth noting by all means feel free to say so, I just noticed moves 9 and 10 as standing out against me in that game.