Sure enough, if you model life experience as a 2d plot, you are going to have to simplify things quite a bit. Yes, time "felt" longer for a child (especially when the child has to wait or wants something yet to come, less so when it's time spent on video games), and children are particularly impatient compared to adults.

But is that experiencing life, though? How many strong memories from that "logarithmic first half" of my life do I have? Actually very few compared to what came later, and they are not particularly compelling either.

My guess is that the author just hit mid-life crisis after having spent one or two decades in an office. Boring mindless job is what makes life experience to plateau, not adulthood. If I think of the most accomplished persons that I know, who've done many things with their life, I can't imagine them saying that their childhood was half of their life. They would probably laugh at the idea.

Or maybe he hasn't reached that crisis yet, since he finds solace in the idea that his child is doing the living for him. Wait until the kids leave home, for the log to turn into a exponential panic.

I think you nailed it. This person is not living, and may never live. When their birds fly the coop and, worse, when they themselves retire, they're in for a whole world of emptiness.