Indeed they are similar! That particular Kyrie is called Cunctípotens Génitor Deus, one of many Kyries in Gregorian chant.
What they did, back in the Middle Ages, was borrow it from Gregorian chant, slow it way down, and resurface it with a second voice in a medieval improvization technique called organum, a well-known feature of Notre Dame polyphony, as Christophe mentioned. If you reverse the process by speeding up the Kyrie recording fast enough, the lower voice will sound nearly identical to this chant.
Organum is considered accompaniment, so it does not technically classify as plainsong, though it is based upon the same. While there are simpler organal accompaniments in 9th and 10th century Gregorian chant, the more florid "Gothic" Kyrie leans far closer to the polyphonic side of the spectrum. Keep in mind, at the time it was composed, plain vs. polyphonic was not a hard and fast division between genres, but rather just a simple matter of whether the cantors felt like spontaneously improving the music that day in church.
The term "Gothic chant" appears to be novel. I could trace it only back to Callixtinus' YouTube channel. I wouldn't be surprised if the term originated there. A web search reveals it hasn't been used in any context that wasn't influenced by Ensemble Organum's popularity on the web.
By the way, yes, Roman chant is synonymous with Gregorian chant ... most of the time.