(This is in comparison to MTG rules, which normally stipulate "... in addition to its other types" for effects like this.)
The original faction is still applicable. Note the exact wording of Hedron Link Device. "You may treat all Constructs as Mechana Constructs." Both the "May" and the "Treat" here mean that the original faction is still applicable. First off, it is "May", so you can just choose to not count it as Mechana at the moment if it will make your Golem better. Second, it is "treat as", which is not the same as "becomes."
In comparison to MTG rules, some cards have the ability "You may cast creature cards as though they had flash." Note that this does NOT give your creature cards flash. It just lets you cast them like they did.