Protein food eating tendency
Proteins are actually pretty calorific but indeed much less than fat. From wiki > food Energy



However, we crave for proteins for other reasons. We digest proteins to get their building blocks, the amino acids. With these amino acids we can rebuilt our own proteins. Proteins are at the very center of our metabolic activity. From wikipedia > protein


  Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, responding to stimuli, and transporting molecules from one location to another.


Many of our DNA sequence are called protein-coding-sequence (often just called gene although definition of what a gene is vary quite a bit). Those sequences are transcribed into mRNA and then translated into protein in order to have some effect on our body. A protein could be an enzyme for example.

For more information on the role of proteins in living organisms, have a look at an intro course to Biology such as for example those of Khan Academy. Khan Academy > macromolecules > protein and Khan Academy > Central Dogma.