About files in /usr/include/x86_64-linux-gnu
According to an answer to a similar question on stackexchange linking to the debian wiki the x86-64-linux-gnu folder is for the linux multiarch implementation, ie supporting cross-architecture dependencies.
from debian wiki: "Multiarch is the term being used to refer to the capability of a system to install and run applications of multiple different binary targets on the same system"
There's a more detailed explanation here, from this stackoverflow post.
EDIT: here's an ubuntu wiki post about it, probably more relevant here