It’s *.jpg so it means you have 256 levels of grayscale (since it’s 8 bit picture and it has only one channel) because of that u can see the isohipsas insted of nice gradient. Try using some format that will store more depth in grayscale such as tiff, exr, raw, psd. Or anything that can stor 16 bit float or 32 bit float infromation (but i think blender cant handle 32 bit images in displacement).
Its possible to take an 8-bit image and blur it an application that can work with 16-bits to get rid of the stair step effect … might work OK for this image, but its definitely a cheat that’s not going to work well with some images.
If you converted the 8-Bit to 16-Bit, it still only contains the 8-Bit values, just at a higher precision. If you want to use the same image you need to smooth it somehow to even out the stair stepped values.