Technically this procedure (I didn't read the article, but I know of this procedure) can only provide female offspring. So yes, the human race technically could survive without men, but they would never be able to produce men. Perhaps they could bombard the embryos with testosterone and hope to confuse the chromosomal messages in mitosis and somehow create a man with XX chromosomes (which is possible) but without the Y chromosome, which as far as I know cannot be synthetically recreated from a female gamete, it would be extraordinarily hard to creat men from 100% female biological material.
As for making egg cells for gay men (as was suggested by another poster), this is not possible using simply the material from sperm. It really only goes on direction (female gamete to synthetic male gamete) as far as we understand with current medical knowledge.