The smallest implementation of full chess is an irrelevant question. It all depends on the underlying machine and how the instructions are designed. At one extreme, a closed circuit with no programming interface but with the ability to play chess is a chess implementation with code size 0.
A legitimate and interesting question is what is the smallest possible chess implementation in a particular instruction set architecture such as x86.
A comparable example is writing quines (a program that outputs its own source code without reading itself from a file). It is a badge of honour to write the shortest quine in a particular programming language but comparing the length of a python quine implementation to a Java implementation is pretty meaningless.
A legitimate and interesting question is what is the smallest possible chess implementation in a particular instruction set architecture such as x86.
A comparable example is writing quines (a program that outputs its own source code without reading itself from a file). It is a badge of honour to write the shortest quine in a particular programming language but comparing the length of a python quine implementation to a Java implementation is pretty meaningless.