It's all to do with the profile applied to the raw files and guesses other software makes as to what that profile ought to be...

RAW is not an 'absolute' format in terms of the image displayed, it's raw data to which an 'opinion' of what the image ought to look like can be manipulated from. It will already contain several view options added by the camera, based on the photographer's pre-determined settings, but these can be changed later, in software.

Adobe RAW in Photoshop will make a guess at what it thinks the Nikon default profile ought to be and what adjustments the photographer may have made to their settings, but frankly it usually makes a horrible mess of it, because it isn't the same as Nikon actually use, it's an attempt to reverse-engineer how Nikon does it. Photoshop interprets the profile as being Adobe RGB(1998).

By the look of it, Paintshop Pro has even less of a clue as to what it really ought to look like. I don't have Paintshop to be able to examine what its guess was.

The only app that can actually guess correctly is Nikon's own software suite, including ViewNX-i. ViewNX-i knows exactly what the camera's settings were, including that the photographer was using the Vivid colour profile addition, for extra colour-punch...

To get that data into Photoshop or Paintshop correctly, the best way to do it is to export as a TIFF... then it will open looking something like it was intended, without having to make any guesses. The correct Profile is now showing as Nikon sRGB 4.0.0.3002 when imported to Photoshop.

On the other hand, the jpgs have been saved, imo [see below] directly from the camera, with the internet standard sRGB profile. This, allowing for variance in actual monitor calibration, is the closest you get to the artist's actual intent, without having Nikon software to interpret for you.

NEF interpreted by PhotoRAW

TIF after export from ViewNX-i with no adjustments

JPG, for comparison

As you can see, the TIF has more in common with the JPG, though the JPG is slightly darker in the greens.

I cant really post a picture of what the image actually looks like in ViewNX-i because the screen layout won't let me drop the size down and conveniently place the histogram over it like I can in Photoshop, but in fact the jpg is the closest of the three to what it looks like in ViewNX-i, so the camera has done a pretty decent job of conveying in a more 'portable' format [sRGB JPG] what the photographer's intent was according to his camera settings.