Not necessarily since you don't need to know Giant to do rune magic.You seem to have skipped over this part in the post you quoted, from the UA:
“Though the tradition originated with the giant rune casters of old, runecraft magic has expanded to encompass countless languages and practitioners across different worlds.”
Doesn't this explicitly say that Giant Magic Runes are no longer needed for rune magic? Listen, I am fine with your approach, I just don't think it is the default assumption of the designers.
Based on that sentence, multiple cultures of rune carvers could be still using the Giant symbol for "Fire" for the fire rune but calling the rune "Fire" in their own language.
There are runes for the 6 giants in the Ordning but no runes for dwarven things like Axe, Forge or Good or elven things like Wood or Fey.