According to what I've just read, none of the negatives have been discovered, just the prints and he wasn't known to be a photographer -- so the rest of this will be guess. The reports do say "gold-toned gelatin silver prints from glass plate negatives." This probably accounts for some of the tones in the prints, but I don't know anything about the process used.
Based on the descriptions and some of the dimensions mentioned, I would guess a 4x6 view camera with the prints being "contact prints" -- so no enlargement of the captured image at all. In my experience with a 4x5 camera, contact prints (because the negative plate is in contact with the light sensitive printing paper) allow you to more easily get an nice print (the image is at its native size, and no issue with having to pass the image through an enlarger's optics).
If you look up other examples of "1900s glass plate prints" you can find images that look similar or better, so I don't think it is astounding that the images don't look worse than they do.
Note -- if you like these images, you might want to look up Edward Weston, he also did still lifes but with somewhat more modern equipment and it is pretty well documented what kind of equipment he used.
More info regarding Charles Jones can be found here. In this article, the collector who discovered them compares both the composition and the process used to make the prints to Eugene Atget. We know that Atget used a large format wooden bellows camera with rapid rectilinear lens and dry glass plates.