Not based on the Minecraft engine. The Minecraft engine is proprietary and closed-source. Also, it is (according to the developers) a bit of a runny mess, so licensing doesn't make sense either.
Leveraging "a bit of a runny mess" doesn't sound like it would make progress quicker. And, once the voxel rendering is implemented, is there that much more for this game to borrow from Minecraft?
I hope they borrow ambient occlusion. It makes it possible to see the edge of a voxel that's in front of an identically colored voxel, and makes the whole game much easier on the eyes.
According to the readme, it's based on an open source engine called Voxlap, created by Ken Silverman (the guy that wrote the Duke3d engine). Here's a link:
You're right in that this is a new engine, but the fact that minecraft's engine isn't open source doesn't necessarily come into play here. There's closed-source engine licensing happening everywhere.