Nikon DSLR.I'm getting some moire while capturing photos from my laptop screen

Is this normal? I just bought a NIKON D5200… Is the camera defective? Or is it just a defect of all dslrs?

Yes, this is very normal. It can be explained by physics/sampling theorems. Since your computer screen is made up of dots (pixels) and your camera sensor also is made of dots, you will get aliasing which creates Moire patterns. When you get aliasing, this also means you have a sharp image. A slightly out of focus image will not show alias issues.

If you use Windows operating system, you can capture your laptop screen by pressing the "Print Screen" key twice in rapid succession. This will store the screen to the clip board. You can use MSPaint and paste (Ctrl-V) clipboard contents to MSPaint. You can also paste clipboard contents to Photoshop.

If you only want to do a screen capture of the active window, then use Alt-Print Screen.

I'm sure the MAC has something similar to this, but I don't know anything about the MAC OS.

When viewing any photo at less than full resolution you can see moire. I suspect your computer's display is producing the effect, not the camera.

Try a different resolution in the camera or resize the photo viewing app in your computer and you will likely see the pattern change or disappear.