First of all, I do not think they've been pursuing that to the degree that you think.

But even assuming that's the case, the natural thing to do in that scenario is to not contribute to the development of the doomsday device. But anthropic's approach seems to be to help build the supposed doomsday device faster?

The only generous interpretation is that Anthropic thinks that only they, the people at Anthropic have the morals/intelligence/whatever needed to build the doomsday device ethically, which is basically the perspective of an egoist despot and which should terrify you.