To me, "Machine Intelligence" sounds less worn than "Artificial Intelligence", and also seems to more strongly imply that they're talking about general intelligence rather than narrow AI. But I don't know whether those were the actual reasons.
I was under the impression that this use of the word "machine" was archaic -- it was used decades ago for naming things like machine learning, machine translation, and the Association for Computing Machinery. I don't immediately see why a more familiar term wasn't used.
http://singularity.org/blog/2013/01/30/we-are-now-the-machine-intelligence-research-institute-miri/
As Risto Saarelma pointed out on IRC, "Volcano Lair Doom Institute" would have been cooler, but this is pretty good too. As the word "Singularity" has pretty much lost its meaning, it's better to have a name that doesn't give a new person all kinds of weird initial associations as their first impression. And "Machine Intelligence Research Institute" is appropriately descriptive while still being general enough.