This is the area we receive the most questions about: installation.
The docs site says Python 2.7.9+ mainly because of out QA environment. I have seen an installation and runtime environment of GWE succeed before on 2.7.3, but this version of python is not tested with the same degree of scrutiny as 2.7.9. You can certainly try it out and, if it works, I'm fairly certain it will be fine.
Since you seem to be building your linux image yourself, there are other dependencies that GWE needs such as the json module and other modules that are generally considered to be in the standard canon of modules. If you see installation issues due to things like ImportError, you are likely just missing a module and need to add it to your linux image with your toolchain (bitbake, buildroot, yocto, etc.).