12 yo beginner game against engine

That name was chosen long ago when I was much more immature and flashy than I am now.

OK, then my response will have a different tone, which is essentially thus: that you cannot tell for someone who has been playing for 4 months! Only after about a year can you begin to talk about rate of improvement. Until then, things are completely unpredictable (in my experience). He has made above average progress but nothing to be alarmed by.

I would suggest that he is indeed good enough to get an account here on Chess.com and should start playing with some serious players. The true potential of a player - in my opinion - is judged by his ability to learn from games against those stronger than himself. So we can talk about how far he can go, once we watch his improvement when he plays against 1300-level players.

For interest's sake, this is a game I myself played when I was around 11 and had been playing for about 7 weeks. (10 minutes a side - in those days I only played blitz whereas now I only take long chess seriously. I played White)

I think you will agree this is a higher level than your cousin right now. And as you can guess I am still extremely far from approaching Fischer! :p So do not demand great things from the boy just because he's had a nice start.

No, not at all.  I really like moves such as 11.d5, but the other kid made even smarter moves.  Ok, now you are surely better than you were at your 11, but I'd advise everyone at that level to play some games without time control (1-3 days), so you'll have the opportunity to think deeply for every single move and plan your strategy via the "analyze".  That's the way I I made myself better 

Hmm that doesn't really simulate OTB play though. Maybe you are right but kids would definitely prefer to get better and play "proper" (i.e. timed) games at the same time. Obviously 10 minutes is a little short. (I recognize I probably should have preferred longer games then, as I do now.)

11.d5 seems a purely tactical attempt to "do something cool" by attacking the Queen. This is the sort of thing the other kid did a lot, and often better, but I personally find it wholesomely weak.

If you look at 17.Nxd5 however you see evidence that even at 11 I calculated an exchange ahead and saw I could win a pawn. Examples of the current 12-year-old doing that? 31. Kf2 ... at 11 I recognized I could let the second pawn come down and threaten mine, and still end up defending it if my King were up there. Where does the OP's cousin play something like that? In my opinion, the difference is clear in the way we won; OK so I never attacked quite like the boy, but my win came because I calculated three moves ahead to win of 1 pawn and in some tight situations I was able to outmaneouver my opponent, whereas in the case of the OP's cousin his wins are the result of 1-move "piece-hang" blunders. I think before we judge him as a great talent we need to see him winning without his opponent blundering. :)

I think I was not bad at 11 but not very great either, so there's no reason to get ahead of ourselves with this 12-year-old. Nonetheless the most important thing to do is not to judge him now but to try and help him improve, and to do that he needs to play tougher opponents - ones who won't blunder.

He plays against tougher opponent against which he loses 100% games. That's the problem and one of the reasons I introduced him to chesskid.com (I said that before anyway). ;)

I don't play seriously in live chess. I'm fine if you don't believe this statement, I would too if I was you, but just setting the record that I play MUCH better in OTB. On chess.com I just make random moves and blunders.