Are there any Intel x86_64 based CM that is compatible and fit for use with Turing Pi 2.x ? I am not looking for performance, more about supporting binaries that are compiled and available only for x86_64.

probably not, these are the only modules officially supported: https://docs.turingpi.com/docs/turing-pi2-supported-compute-modules I do wonder what sort of software you need to run. In many cases you should be able to compile for ARM with little to no changes if you have access to the source code