It doesn't seem to been used in early tabletop gaming naming conventions (for instance, in Dungeons & Dragons and directly inspired games) but was already seemingly omnipresent in the 1990's fantasy games, especially video games.
What made "mana" such a standardized name for a gameplay concept, virtually identical to "magic", rather than other terms associated with spiritual power (such qi or ojas) critically in a "lay" form (as XVIIIth century "magnetism") rather than associated with religious belief ?
This answer of /u/King_of_Men/ answers your question:
https://www.reddit.com/r/AskHistorians/comments/a45gwf/mana_is_a_real_concept_from_polynesian/
Hargrave's 1977 "Arduin Grimoire", an alternate "D&D" ruleset, included the use of "mana points" when casting spells.
Note that this is just a few years after the first edition of "Dungeons and Dragons" itself.
A quick look at a scan of the 1977 edition of the "Arduin Grimoire" found references to "mana cost" for spells on page 22/50 in the PDF: https://i.4pcdn.org/tg/1418437896796.pdf