Without more context, it's probably figurative and used for emphasis.  And yes, you could say that both "on earth" and "in God's name" can be used as intensifiers in this sentence, but I think "on earth" implies more incredulity while "in God's name" is more like regret.

> on earth: *What* is the nature of this thing that we have done?

> in God's name: *Why* did we do this (stupid, horrible, some other negative descriptor) thing?

It seems there is a slight difference, but I'm not sure if I've defined it well.