I think the author's real problem is less his age but his tendency to stick to rules which are just meant as "rules of thumb". He says that this is how he is thinking but still primarily blames his age.

Following rules and schematics in chess is great/necessary for end games (which he says he wins) because there you really just work through the algorithms and it also allows for quickly played openings (assuming you memorized the few standards that are played 99% of the games).

But in mid-game you actually need creativity and concepts like forks become much more important and I'd trade a "knight on the rim" for a choice between two forks the next move any time. His daughter seems to be playing with creativity while he is so stuck in schematic play that his daughter can even predict his moves (“I knew you were going to do that.”).

What I think is really curious is his remark: "She played [...] as if I were just some lower-level chess engine making haplessly random moves. Indeed, when I made my moves, her eyes would often drift elsewhere—as if what I was doing was almost inconsequential to the larger game."

She is right to do so, nobody cares about what one did 3 moves ago. The board is in a state that does not care about its history, it only cares about future possibilities :) When I play chess and look at the board when it is my opponent's turn, I don't care for my opponent but just take the time for a deeper analysis.