I wonder sometimes about the validity of comparing the older jumping records to the heights today, just because of the difference in the construction of the jumps.
The old jumps weren't vertical. They had that ramped front so the rider could run down to the base, and still have the highest part of the horse's jumping arc be over the highest part of the jump.
And it looks like those rails were secured so that they would absorb a pretty good rub without coming down, as in the first video with the gray horse. The top bricks of a wall, which is usually used these days for a high jump, come down pretty easily.
If you look at that 2.4 m jump, it is completely vertical!
The wall in the second video is vertical.
The ramped jump in the first video is not. Many of the older records involve jumps like the ramped one. And for sure, the top rails on the ramped jumps were secured differently than the bricks on top of a wall. That's my point.