This claim appears to be two claims, in fact. The first is that BBG inhibits P2X7. The second is that P2X7 assists ATP in killing undamaged motor neurons.
According to a Google Scholar article I found, http://molpharm.aspetjournals.org/content/58/1/82.full
"In this article, we show that Coomassie Brilliant Blue G selectively inhibits P2X7 receptors with nanomolar affinity."
So there appears to be at least one study showing the first claim to be true.
Claim 2: From the same paper at http://molpharm.aspetjournals.org/content/58/1/82.full
"P2X receptors are ATP-gated ion channels that are present in both excitable and nonexcitable cells. Their activation by extracellular ATP opens a cation-selective channel that also allows significant calcium influx. P2X receptors mediate fast excitatory transmission at sympathetic neuromuscular synapses as well as at some neuroneuronal synapses in the spinal cord and brain. There is also good evidence to suggest that they may be involved in other physiological and pathophysiological functions including pain perception, endocrine and exocrine gland secretions, and release of interleukin-1β from immune cells"
This shows that P2X receptors do act with ATP to perform actions in nerve cells.
Later in the article, it is mentioned that
"P2X7 receptors are functionally different from other P2X receptors, because their activation leads to the formation of a large pore that allows passage of molecules up to 900 Da and subsequently rapid cell death"
This raises another question of "does such activation regularly kill the cell with the P2X7 receptor?" It can kill, but does it? This, I could not answer. I will look for more information when I go home.
It's also interesting to note that, per http://www.ncbi.nlm.nih.gov/pubmed/22963440,
"P2X7R-deficient mice display a marked attenuation of inflammatory responses, including models of neuropathic and chronic inflammatory pain"
So it's not all positive when one inhibits P2X7.
So it would appear that yes, BBG inhibits the activation of P2X7 receptors, and that yes P2X7 receptors are responsible for the quick death of cells.
My final comments: it's grossly misleading that the article starts with mentioning how blue M&Ms are different than the rest, then mentions that the dye used is "similar to" BBG. "Similar to" is a weasel phrase. BBG might be useful, blue M&Ms are not necessarily. There's also not necessarily a metabolic pathway from ingestion to the spinal cells where BBG could inhibit the P2X7 channels.