I see no indication that those were ever referred to as "metric" systems.
the term "metric" can be defined many different ways. Per Merriam-Webster - "a standard of measurement <no metric exists that can be applied directly to happiness Scientific Monthly>"
Seeing as how the Japanese and Chinese systems are quite standard (at least in their own right), you could imply upon them being "metric systems of measurement".
Hell, the base of the word metric is metre.
Wrong.
Per Merriam-Webster again, the etymology of the word metric is as follows:
Greek metrikē, from feminine of metrikos in meter, by measure, from metron measure
First Known Use: 1760
So it would be safe to infer that the ancient Greeks would have used the word in such a way as to mean "a measure". Indeed in Network and computer systems, the term metric is used to state a measurement, not a specific system of measurement.