Once: My friends, what we have in front of us is quite a remarkable thing. This is not a game, it is chess history.
Let's deal with the "not a game" thing first. There is a strong possibility that this was never actually played, but was composed to show the mating tactic. That is probably why NN played so poorly - not challenging white at all, castling into the attack, allowing his Nf6 to be kicked out of the way, grabbing the Ng5 (which in turn opened the h file).
No, this is almost certainly a composed game, carefully devised to show the greek gift mate in a short game.
The date we have for the "game" is 1620. That's not twenty past four in the afternoon and time for tea. It's 390 years ago - men wearing tights, Shakespeare has just died and the Pilgrims are setting out from Plymouth. And everybody is saying things things like "verily", "forsooth" and "prythee" instead of "like", "cool" and "djaknowwhatImean?". And the nearest thing we have to an ipad is a well-trained messenger pigeon.
Greco was quite possibly the first ever chess professional. So how do you earn a living at chess before tournaments were invented? You need to exploit the age old concept of supply and demand. Even back in 1620, you had people with disposable money who wanted to play better chess. And Greco was the opposite - someone without money who could play ... quite a bit actually.
So Greco looked for sponsors - the Nike and Coke of his day. And no doubt his sponsors came from wealthy landowners, merchants and nobility. To repay his sponsors he would make guest appearances, play matches, give lessons and hand out these little handwritten "games" to amuse, educate and keep the gold coming in.
So when we see today's puzzle, we shouldn't just yawn and say "uh, uh, another greek gift". This was quite possibly the first ever greek gift, played by the eponymous Greek, a middle-ages Hello magazine spread, a television commercial celebrity endorsement (long before television was invented). It's just a man earning his living, feeding his family, paying the mortgage ... a blue collar Joe wearing doublet and hose instead of jeans and T shirt.
Then I take a look at the bookshelf behind me ... around 200 chess books all written by better chess players than me, all promising to make me a better player, and each one doing exactly what Greco was - making a living in this world.
I sometimes envisage chess as a massive and mythical pyramid made of human bodies. At the bottom are us humble kibitzers, buying the books, reading the websites, paying entrance fees, pushing wood. And standing on top of us are the professionals, making a living out of the fact that we want to improve. And higher still we have the elite and standing right on top is the world champion.
And if you can hold that image in your mind, Greco was quite possibly the first chess player to climb onto someone else's shoulders.
And the game you have in front of you is how he did it.