There are people who do all that you describe with a smaller slip-joint, from food prep, cleaning small game and making shavings for fires. So, the 113 will certainly handle the job.
I would say that the number one attribute of a good camp knife is that it makes you happy. You find the 113 to be beautiful and that right there is all the reason in the world to just go with your heart and get it and enjoy it.
One thing I find fascinating about knives is the trade-offs they need to deal with. What makes a knife excellent for one thing can make it less excellent for something else. So the first question I would ask is do you plan on the 113 to be the only knife you have with you when you're camping? If so, I think you're on the right track. Personally, I prefer a bit more blade for food prep and a bit more handle for my Xl sized hands. I have a fixed blade not terribly different from the 113 and given the choice for one knife for camping (and no splitting), I would and do choose my 110 every time. If the idea of a bit more blade and handle is appealing and you want to keep the stunning looks of the 113, you might look for the limited run of fixed blade 110s that Buck recently put out. This isn't advocating for the fixed blade 110 over the 113. Just noting that it's out there as an option. If your hand fits the 113 well and you can live with a 3" blade for food prep, the 113 would be a more compact package.
The second question I would ask is what is your preference in terms of carry? Pocket or belt or pack? I've been carrying knives my whole life nearly and have never taken to belt carry. I prefer a knife either in my pocket (right rear preferred with seam run up the pocket to hold the knife upright) or in my pack. When I'm outdoors, I always have a pack with me ranging from a small fanny pack to a large external frame, so the decision for me is a folder on my person (in my pocket) or a folder or fixed blade in my pack where I need to go and get it. For me (just my testimony) for camping, I prefer to have a pocket knife on my person and when I'm backpacking or hunting, I prefer in-the-pack-carry and am more apt to carry a fixed blade. I like the easy access of pocket carry when camping. If belt carry works for you, this question is moot and if you're not sure, there's no way to tell other than trying it which says, just get the 113! But it is worth noting that there are a lot of Buck folders that will do all the things the 113 will do if you take battoning wood off the table including the 110, 112 and 500 - all beautiful in their own right.
As for splitting down kindling... I use a long handled hatchet, sometimes called a boy's axe, for splitting camp wood and breaking it down to kindling. We rely 100% on locally purchased camp wood in New England due to pest controls and that wood is always pre-split into fireplace size but then needs to be further split to kindling. The boy's axe handles that fine.
But, I find it tedious to use a hatchet, even a good sharp one, to split kindling down from the 1" diameter down to pencil sized sticks. I find that my 3" hollow ground fixed blade (not entirely different from the 113) handles this fine so long as I don't force it through hard knots. I've come to stongly prefer a thin convex sabre grind for my camp knife over the hollow grind, but that is YMMV sort of thing and not a reason to not get the 113. The 113 is up to the task of splitting down small kindling to pencil size and in this way, would be better than a folder.