The way Steve describes what he suspects memory will be like as we continue to increase our lifespan is closely analogous to what happens in artificial neural networks - perhaps not very surprising since these are loosely based on biological neural networks. When you train an ANN to perform a certain task, the order in which you provide the training examples can make a huge difference in your eventual performance. For example, let's say you want to teach your ANN to learn to distinguish images of dogs from images of cats. If you first provide it with all the dog images and then with all the cat images, the ANN will probably not perform very well. Earlier experience tends to be slowly overwritten by / merged with later experience. If the latter images are all cats, then that is what the network will remember best. A better way is to randomize your training examples so that the cat and dog images are more or less randomly distributed, so that the memory of both is roughly equally "fresh". This also means that, if you want to train the same network to perform a more expansive task (e.g.: also distinguish horses from dogs and cats), you have to keep re-feeding it the old training examples. The networks can, re-use the commonalities between the different tasks (e.g.: being able to detect lines, blobs, or even more complex structures like eyes), and use them to generalize, which makes subsequent learning potentially more efficient.
Of course, I think we have this kind of experience even over the course of our own, still shortish lives. Over the past few years I've been reading a ton of science and watching many lectures. I find it super frustrating how my earlier knowledge keeps fading so fast. I make some progress (I'm certainly capable of understanding some things a lot better now than I could a few years ago), but it's so much slower than I'd like it to be because I keep forgetting things I learned previously and having to come back to them. And I know that as a kid, I used to know pretty much everything there was to know about my then favorite comic book series (Suske & Wiske), including matching all the titles to their issue number. I was able to do that without effort for years, but now -even though I still do have the comic books somewhere- I don't think I could match any of them if you put a gun to my head. I also used to be able to say exactly which actor had played in which movie that I had seen, more or less regardless of how often I'd seen that movie or how long ago it was. Nowadays, I barely remember movies I've seen just a week ago. Some of that has to do with the fact that I got a projector at home now, so I just watch a lot more movies, but it kind of feels like my brain's wiring has changed a bit. I used to be good at remembering little bits of information. Now, I'm crap at that task, but I've become much better at finding the common threads among many distinct bits of information and putting them into a coherent picture and fitting that into the overall narrative I have from my general knowledge of the world.
Season 9 of Doctor Who is on Amazon Prime, so I've been watching, and the episode "The Girl Who Lived" addresses this issue.
At the end of the previous episode, "The Girl Who Died" the Doctor revives a girl who had died defending her Viking village, making her immortal. 800 years later he encounters her again.
The girl, being immortal, has kept journals of her life so she can go back and remind herself of stuff that happened. Otherwise, she cannot remember the first 9/10 (?) of her life. She's forgotten her Viking village, even her birth name. There's just too much to remember and it fades away with time.
I wonder if Steve was influenced by Doctor Who, or if this is just the obvious conclusion. I remember a few incidents from my childhood, but mostly I remember none of it. When I go back just 25 years and try to reconstruct the timeline of important events in my life, I cannot fix a number of them in time. I kind of remember my childhood home, but nothing of the day-to-day events. I remember when my finger got smashed in the door of a derelict car we were playing around, and that I needed one stitch, and the day my friends left me stirring a bucket of plaster-of-Paris and then never came back because their mother would not let them go back out. But what of all the other days? Nothing!
If I lived to be 800, would I have any memory at all of any of my favorite hiking guides of the past decade or the hikes they took me on? I suspect not. Unfortunately, I'll never have the chance to find out, since immorality is a pipe dream.