You make my point for me.
Carrying a knife of some sort is on pretty much every version of the "ten essentials" since Harvey Manning and Seattle Mountaineers first wrote about it in the classic, "The Freedom of the Hills".
The requirement to have a locking knife is a bit odd, but whatever. As you note, the race organizers accepted a small folder.
If having a knife is considered an essential, and one wants maximum safety, than a fixed blade will offer that; no lock to fail, or possibility of a slip-joint accidentally failing due to improper use in a moment of panic.
As for what minimalist camping is, I guess that's going to depend on what one is comparing it to.
When I went to a cabin with a couple of friends, the amount of stuff one brought was phenomenol.
HUGE piles of stuff.
When that same friend came out winter camping, the amount of blankets, groundsheets, insulating material and blankets he carried out into the woods was quite staggering. He admitted once he got there that such things turned out not to be needed (as we had crafted a nice warm shelter), but he hadn't gone winter camping in decades, and didn't want to freeze to death.
So compared to that, bringing a high-quality tent, one sleeping bag, a stove of some sort, dehydrated food and water filter would be minimalist for sure.
However, some other guy would scoff at that, and say that a knife, some food, and a cup to boil water in was minimalist.
And then some other dude would trap a squirrel with a snare made from braided bark, skin it with a flake of sharp stone, and roast it over a fire started by friction...and possibly laugh at all of us (except he's so hard-core he doesn't own a computer

).
Me, I like to just add a big knife, some food and water into the same backpack I ride the bus with, and wear the exact same clothes I wear while waiting for the bus.
That's how I like to do it.
Well, a tarp is nice too in case it rains.