Well, considering that we have very little evidence about what what Roman Music actually sounded like (credit: /u/flotiste) it's pretty safe to say that, no, this is not an accurate replication of Roman music. Rather, what this seems to be to me is a 20th / 21st century film music tradition of "Ancient^^TM Sounding Stuff." That sound is pretty generic and can be used for everything from Spartans to Dothraki. This sound isn't necessarily trying to be authentic, rather, it's trying to signal to its audience that it's 1) "foreign" (ie, not something movie going audiences hear very often in day to day life) 3) "old", and 2) "epic." The first is accomplished in your pieces by basing the riff on a tritone (I'm hearing a scale such as C D Eb F Gb as underpinning the riff, though I gave it only a cursory listen), the second is accomplished by the use of a drone and doubling the guitar in unison with a male choir (perhaps a vague allusion to gregorian chant?), and the last is accomplished by having the riff be a rhythmically "plodding" and "heavy" thing that repeats incessantly, along with various orchestral signs of epicness.

But, to get back to your original point, this is picking up on a tradition of representing the ancient world and communicating that representation to a movie-going (or video game-playing) audience in terms they would understand, not trying to accurately depict what ancient Roman music actually sounded like. At best, it may use some ancient roman instruments (or something that can imitate it reasonably closely) as part of its orchestral color. I suppose that that's reasonably "authentic" given that that's one of the few things we can recover from the era. But that's like saying this is an accurate depiction of 13th century Scotland just because it uses bagpipes.

Now, an interesting project would be to trace the tradition of this sound within Hollywood. How and when does it develop? What differences (if any) do film composers use to differentiate between, say, Rome and the orcish Horde of the Warcraft universe? This unfortunately exceeds my area of knowledge, so I won't be of much use here. But (and this is speculation), it does strike me that the metal genre has a long fascination with "Ancient^^TM Sounding Stuff" (this stretches way back into "pre-metal" hard rock days to things like Led Zeppelin's "Battle of Evermore") and the means they use to depict that may have fed into the sound that Hollywood developed. So there may be something of a feedback loop here that would be interesting to tease out.

But no part of that depiction is rooted in the authentic musical practices of ancient Rome.