Fluency is a concept related to flow, and those two words share a common Latin root. The speaker is obviously perfectly fluent, but could not quite pass for a native speaker. There are a few minor incorrect phonemes, but mainly it's a matter of intonation or cadence. They remind me of Russell Peters doing his superb Chinese accent.
Russel Petters does multiple accents very convincingly. Much of his material centers around the differences in languages and accents, but what makes it so good is that it's often based on actual phonetic aspects - he'll riff on phoneme confusion, aspiration, glottal stops, tonal languages, inflection, rising/falling pitch, and other similar aspects. He's either a very astute observer, or has studied some on phonology and phonetics. Perhaps some of both.
When he starts teasing someone about it, they can't really get too offended, because all the points he makes are valid and based on actual pronunciation issues. He'll joke about the difficulty understanding a particular accent, all while explaining exactly why it's hard to understand, but using lay terms to explain linguistic terms. He's brilliant.