What is that camera?
The camera you've pictured appears to be a Nikon D750.
How many cameras these days have it especially Nikon D5300?
Well, pretty much all digital SLR cameras have full color screens so that they can display image previews. How much color they use in their menu and control screens is a bit more variable.
This YouTube video about the D5100 shows the Information Display with a similar color background to the image you shared above.
The Information Display screen for the D5300 appears to be a bit more subdued, at least as shown in this review of the D5300.
The Nikon D5300 Reference Manual, page 197, shows several display options for the Information Display screen, though. In addition to the "classic" option shown above, there are six "graphic" display options, three of which appear to be similar to the example you showed from the D750. Unfortunately, the manual is in grayscale, so the actual color schemes of each option can not be determined from the illustrations in the manual.
Will my Nikon D80 have that color option?
Earlier Nikon DSLRs like your 80D did not offer this Information Display option on the rear LCD screen when shooting with the viewfinder. Most of the same information was displayed on the monochrome 'Control Screen' located on the top of the camera body. When one delves into the actual menu options with the newer cameras, they look more similar to your Nikon D80's menus as they are displayed on the color rear LCD screen.