Help me reconstruct (a puzzle of sorts)

Can you recreate the entire game from the information presented in this image?

I might add that I know the answer. This instructive miniature is one of my favorites. I first saw it in 1975 while playing through the game in Irving Chernev, The 1000 Best Short Games of Chess (1955).

Here's one move-order that reaches that position:

1.e4 e5 2.Nf3 Nf6 3.Nxe5 Nxe4 4.Nc3 Nc5 5.Bc4 f6

@Iron-Toad, those moves get us to the position. Do they seem the most likely sequence? I rather suspect that White played 3.Bc4, for instance. In your sequence, wouldn't Taylor have been more likely to play 4.Qe2 or 4.d4?

4.Qe2 appears in several books that should have been well-known in 1862.

For instance, this game appears in several early chess books. London chess players in the 1810s-1820s produced several compilations of games from early Italian and Spanish texts, as well as from what was known of Greco's manuscripts. Surely most decent players had some knowledge of these books forty years later.

This appears in the 1656 collection of Greco, but it may also be in William Lewis' 1819 compilation.

@Ziryab, I must admit I did not try to find  the most logical move order, sorry for my laziness (had just woken up, needed my tea before I could think clearly).  Yes, in the line were both sides capture the e-pawns, Qe2 would be expected, from what little I now of the Petrov defense.  There must be several possible move orders that would reach the target position, some more reasonable than my attempt. But I suspect that you know much more about Petrov theory than I do.

That Greco game is wild -- now I remember why I'm too chicken to play the Petrov.  At first I heard it's  drawish, but like many K-pawn openings, it actually seems very fairly tactical.

@Iron-Toad, now that you are awake, have you found the forced mate in eight? It is a true work of art! I think it took me 45 minutes to work it out at a chessboard some years back. Of course, I should have already known it from that book I read in my youth.

I found the mate quickly (in a couple minutes), but with the help of a chess.com analysis board where I can make moves and don't have to visualise the whole sequence. I will PM the answer to you.

My guess

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I'm still working on it so I'm not looking at the answer above.

I agree with the move-order proposed by llama47 :) And I also found the mate in 8 but I had to make moves on a board to visualise it... This is a nice short game !

That's what Chernev has and they seem the most logical to me. Now, the mate in eight?

I love the anticipation of the pin six moves prior.

I couldn't find the mate in 8 without calculating a long time. I already cheated with an engine.

The sequence is a bit instructive... at least it was for me. I guess because you're actually trying to find the fastest mate instead of like you'd do in a game and just play anything as long as it seems completely winning.

Makes me think trying to solve king hunts like this has some value.

It does. I found a mate in nine fairly quickly. The mate in eight took longer.