I don't think it is non-religious, so much as it is against organized religion. I think they are basically saying is that if you look at the world (which is pretty screwed up) and you look at the organized religions with "lies on the lips of priests" and look at our great cultural monuments, mausoleums with tears on the floor, and Colosseum doors covered in blood, that none of these institutions can really be much of a guide at all.
Their solution seems to be to be to just figure it out on their own: "get the hell up out of your seats, preach", "We formed a new religion". Maybe it's deeper than I am giving them credit for, but it seems that in the end they basically say that since no one has the answer, let's just do what feels right. I don't know, is hedonism a religion?