Why Do My Camera's Pictures Look Like An Oil Painting?

I bought a new camera this past weekend. I had thought I was going to need over a thousand dollars to get a camera which could take really large-sized pictures at an eight-times optical zoom, but this thing has the 8x zoom, and the large picture size is 5152 x 3864, which is huge. So I bought it on Sunday morning, and to my delight, the thing came with a fully charged battery. Or maybe a mostly charged batter, because unfortunately, it only lasted 2 hours of a 6-hour event.
Anyway, here's the real problem: When I zoom to 100% magnification on the pictures I've taken, they look like an oil painting. Of course, I don't have a monitor with 5152 x 3864 pixels, but part of the point of that size is that I can leave space around the subject and then crop to my subject. And the old camera had some really good 100% magnification.
Here's an example of a picture taken with the new camera, cropped to 1024 x 800.

That doesn't look so bad, but when you click on the picture, you'll see what I'm talking about. Or you should.

I've chosen a comparable picture for comparison.
Here's that picture scaled down to 1208 x 800:

And the new camera's whole picture scaled down to 1067 x 800

(Why they have different ratios, I do not know. That stuff should be standard, so sez I.)
Now, here's the old camera, without scaling, cropped to 1208 x 800:

Mind you, the old camera doesn't have 5152 x 3864, so here's a picture from the new camera, scaled to
 3008 x 2000, which is the highest pixel dimensions the old camera can do, and then cropped to 1067 x 800:

Note on the subject matter: I usually dislike posting photos of people without their permission(s). But when you're a college, or professional athlete, competing in an event in a large stadium, which is broadcast on national television, you don't have that same expectation of privacy as the guy who happens to be shopping at the local supermarket.
Note on the post format: I was originally going to put in a table of the photographs, with a row of new camera pictures and a row of old camera pictures and the columns being the full picture, a scaled picture and a cropped picture, or some such, but it doesn't seem like that would really elucidate anything.