heuristic: this game is a good example of "best move" versus "player style". Morphy choses moves that are more in the style of "first develop and then attack the K" as opposed to "best move without strategic objective" (aka chess engines!)
from moves 12... to 16..., Rd8 is preferred by Fritz. yet Morphy is focused on development and K safety (castling).
with help from WHT (17.Neg5 and 20.Kh1), Morphy then focus on "K attack".
He usually does this by exposing the K via clearance sacrifices. 23...Rxg2 shows my thesis. This move is classic Morphy and yet Fritz finds 23...Nf5 is much, much better. (23...Nf5 24.Qb1 Rxa3 25.Qxb7 Nfe7 26.Re3 Rd3)
ditto for 25...Rxh2+. Fritz likes Rg4 or Rg5 by a wide margin.
a major benefit of attack is that imprecision is tolerable, in defense it is fatal. 36...Ne2+, 38...Nfg3, 40...Ne4+ are all imprecise according to Fritz, but each still maintain a crushing attack.
I don't understand Fritz's analysis of 35...Qc4. A Q move to other squares on the f1-a6 diagonal is evaluated as superior to c4!
This is just the observation of an amateur. your mileage may vary!