The brown dwarf "limit" is about $0.072 M_{\odot}$ at solar metallicity (e.g. Chabrier et al. 2000) and is composition dependent. It gets a little higher in metal-poor gas and a little lower in metal-rich gas. $0.064 \pm 0.012 M_\odot$ (the third significant figure is superfluous) is within one error bar of that limit, which in itself is only a 68% confidence limit, not an absolute limit of what is possible. Therefore this object could be a star or more likely, it is a brown dwarf.
The relationship between spectral type and mass is not well established. It requires researchers to actually measure the mass of objects near the stellar/brown dwarf boundary. A spectral type of L2.5 would a priori indicate that this was probably a brown dwarf, and that is indeed what the mass measurement suggests.
The paper referred to by the wikipedia article you cite, in support of a L2.5V spectral type, is by Dieterich et al. (2013). Those authors say the spectral type is L2.5. The wikipedia authors made up the luminosity class.
To establish whether something really was a brown dwarf I think you would have to detect (or not) neutrino emission from its core. A sort-of proxy is to look for lithium. (Old) objects with lithium must have a mass lower than about $0.06 M_\odot$ and are almost certainly brown dwarfs. Objects that have depleted their lithium, which fuses at lower temperatures than hydrogen, are most likely stars, but could just be brown dwarfs. For example, I imagine that this object would have depleted its lithium, so it doesn't really tell you one way or another.
In the end, it isn't hugely important to know. There isn't much difference between a ball of very slowly contracting gas that is approaching its minimum degenerate radius and a slightly more massive ball of gas that has a little bit of fusion going on and a stable radius that is ever so slightly larger.
Postscript: I just checked and the mass determination comes from Filipazzo et al. (2015). This is not a dynamical mass estimate. They use evolutionary models and their estimate of the bolometric luminosity of the object to estimate the mass, assumimg that the age is somewhere between 500 Myr and 10 Gyr. The error bar here is just the range given by these age estimates (an older object would be higher mass). The error bar could be hugely underestimated. When dynamical masses for low-mass stars/brown dwarfs are measured, they are usually considerably larger (by 30% or more) than obtained from evolutionary models, for poorly understood reasons (e.g. Ireland et al. 2008). So from that point of view, maybe this object is a star (with a larger mass).
