Short answer, I agree with you that the "connectivity" as defined in your link should be 2. Here's why I think that:
Step 1: make sure you understand the Euler characteristic.
Step 2: I think that figure means to indicate that those 8 voxels are those under consideration.
Those 8 voxels form a torus, which has an Euler characteristic of -1 (see above). This is deltachi which you should interpret as "the amount that this part of the sample (those 8 voxels) contributes to the total Euler characteristic of the entire bone (the 8 voxels plus the "caps" on either side - indicated by dotted lines"
Step 3: if you add the "caps" you end up with something like a hollow sphere which has an Euler characteristic of 2 =
1 - (-1). Also see above. Hooray!
Edit: Okay, I have to be more careful when answering stuff before coffee. A torus has Euler char = 0, not -1, whoops -I'll look at this a littler more closely
I don't do bone stuff, but this is my best guess. Does this sound like it could be right to you? You could also try making that 8 voxel shape and doing the analysis in bonej and confirming that you get 2 for the connectivity and -1 for deltachi - that's what I'd do.
Good luck, and hope this helped.