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Using the FPGA isn't emulation argument then the CD player doesn't play music as it is converted from analogue to digital and then back to analogue, while the tape stores an analogue wave. In reality they are both lossy audio storage & reproduction systems, but the loss is in different areas.
That's where you're wrong. As language evolves, words pick up new meanings for specific contexts. For example, with computing, you have a bunch of words that existed before modern computing, but that have specific meanings when applied to computers: kernel, shell, mouse, pipe, etc...
Quite right. This is the description of computer that existed at the time of Turing, in his work (and the work of other computing pioneers) he used this earlier definition to convey what was being proposed.