Thirdly, some of the content you linked to uses other, more descriptive, terms to describe what's occurring, e.g. "FPGA-64 is a re-implementation of the Commodore-64 computer using reconfigurable logic chips." Re-implementation is a clearer way of describing the process being followed.
Unless you end up with the exact same configuration of gates, it's not a "re-implementation" in any sense that makes it distinguishable from "emulation". And really, a re-implementation of
what? The hardware? Nope. FPGA-64 makes a particularly interesting example because its SID emulation is not anywhere close to how the real SIDs function. Hardware end-functionality? Nope, even if it's close or maybe even "getting there". End-user experience? Fuzzy, but have a look at the FPGA-64 changelog to get an idea of what bugs they've had to tackle to this day and ask yourself if it makes sense that they are somehow all magically weeded out by now.
The only ways to have these FPGA systems come close to the functionality of the systems they intend to emulate is either to try to get them into reproducible states in synch with the original systems and analyze the differences, or take a microscope to the chip surface.
One will make you insane, the other will not