The Caverns of Thracia is compatible with Original D&D, Holmes Basic, and AD&D First Edition. To the extent that AD&D Second Edition didn’t change much of the basics, it is also compatible with that, and the same is true of the later Basic/Expert/etc. and Rules Cyclopedia versions of D&D.
Thracia reads like a mashup of OD&D and Holmes Basic or AD&D, which is how many of us gamed at the time. For example, at least one encounter (the cleric Holoste from room 84) has their alignment given as Lawful Evil (LE). The two-axis alignment system was created for AD&D, though it first saw print in Holmes Basic. The OD&D and later D&D B/X series used the one-axis alignment of Lawful/Neutral/Chaotic.
Thracia was copyright 1979, by which point the AD&D Monster Manual, Players Handbook, and probably Dungeon Masters Guide had been released (the Dungeon Masters Guide was also released in 1979). This was a time of transition. Dark Tower, released the same year, was marketed as a supplement for AD&D.
According to Jaquays, part of the reason Thracia was marketed as for D&D is that Thracia used house rules, and the licensing requirements for D&D supplements were less strict than for AD&D supplements:
Even Dark Tower got a bit of a reaming from TSR … I was including
house rules elements in my design of an AD&D product … which was
verboten. That’s partly why Caverns of Thracia ended up under the D&D
brand … I could be more loose with my interpretation of the rules.
But the actual adventure was written for the author’s own campaign, which by then had transitioned to AD&D:
Caverns of Thracia was originally intended to be an AD&D title, just
like Dark Tower… My local group had gone 1E AD&D by that point (as
much as we could).
The jackal-headed “dogbrothers” in CoT were originally supposed to be
AD&D Jackalweres. As those were AD&D-only creatures, I had to recreate
them as something else (and I don’t think I could back port the
jackalweres … that wasn’t acceptable).
So it was written with a house-ruled AD&D in mind, and edited with OD&D in mind. It’ll be compatible with any rules set that is compatible with those, which covers most of the OSR rules sets and even second edition AD&D and B/X D&D up to the Rules Cyclopedia.