"Fantastic" vs "Non-Fantastic" goes back to Chainmail1.
The first reference I have (Original D&D) is the discussion on page 3 of the second issue of Strategic Review (Summer 1975) - the newsletter from TSR that had some FAQ for their new game Dungeons and Dragons. The excerpt you are referring to looks like a cut and paste from that article:
Assume the following dice score by the Hero. Note that he is allowed one attack for each of his combat levels as the ratio of one Orc vs. the Hero is 1:4, so this is treated as normal (non-fantastic) melee, as is any combat where the score of one side is a base 1 hit die or less.
What precedes it should answer your question. (The article begins on the bottom third of the left column; what you cited is in the middle of the right column).
Combat: CHAINMAIL is primarily a system for 1:20 combat, although it
provides a basic understanding for man-to-man fighting also. The
“Man-To-Man” and “Fantasy Supplement” sections of Chainmail provide
systems for table-top actions of small size. The regular CHAINMAIL
system is for larger actions where man-like types are mainly involved,
i.e. kobolds, goblins, dwarves, orcs, elves, men, hobgoblins, etc. It is
suggested that the alternate system in D & D be used to resolve the
important melees where principal figures are concerned, as well as
those involving the stronger monsters. {italics mine}
When fantastic combat is taking place there is normally only one exchange of attacks per round, and unless the rules state otherwise, a six-sided die is used to determine how many hit points damage is sustained when an attack succeeds. Weapon type is not considered, save where magical weapons are concerned. A super hero, for example, would attack eight times only if he were fighting normal men (or creatures basically that strength, i.e., kobolds, goblins, gnomes, dwarves, and so on).
Chainmail's original rules were for regular, "non-fantastic" medieval battles; a later edition added a fantasy supplement in the back: it thus added "fantastic" combat (beginning on page 28 in the 3rd edition; not sure if 2d edition page number matches that). Chainmail was the game that informed D&D's original creation (it's more complicated than that, but that's a separate topic).
The distinction, one one synthesizes the above: "any combat that does not involve monsters with more than 1 HD is treated as non-fantastic". This is similar to the "man-to-man" and the battles with Fantasy Combat Table (Chainmail 3rd edition, page 44). Given when your cited excerpt was written, and the edition that it was written for (Original D&D plus Greyhawk (which had come out shortly before that article)) this makes sense.
As we review Monsters and Treasures (the second of three little brown books) most 'fantastical' creatures like dragons, basilisks, ogres, hippogriffs, and so on had more than 1 HD. The bulk of manlike creatures in OD&D (dwarves, goblins, humans, elves, orcs, hobgoblins) have 1 HD or less (with a few exceptions that had 1+1 or 1 1/2).
1 As but one example of where fantastic was compared to (implied) non-fantastic in the Chainmail rules, from pages 38 and 38 of the 3rd edition:
FANTASTIC SIEGES: To combine the siege and fantasy sections, use the following: Dwarves dig twice as fast as an equal number of human sappers. They may attempt 2 more mines or counter-mines than usual. (Orcs dig 1½ times as fast; one more mine or counter-mine.)
