It isn't galangal, although galangal is sometimes referred to as blue ginger. The photo in the original post is a variety of ginger called "blue-ring ginger".
The first time I ran across it was at my local co-op. I bought some, not knowing it was a different variety than normal Chinese ginger. When I cut into it and saw that it was blue on the inside, I thought it was moldy and took it back to the store the next day. The produce manager explained that sometimes their supplier brings it in. It comes in labeled as ginger, and the only way to tell the difference (without cutting into it) is that the blue-ring variety tends to have more slender finders.
From what I understand, it's considered to be the best of the best, and it does seem to have a milder flavor. For juice or tea, I like the blue variety, but to be honest I prefer the regular stuff for cooking.