No, we get an egg (i.e. the part usually provided by the female), which must then be fertilized by sperm.

I don't know enough to say if that allows extracting eggs from males. Could two males have a child together using this technique?

That is a good question. Excepting the sexual ones, all the cells in an organism are diploid¹, including the ones found in blood (excluding erythrocytes, since those do not have a nucleus, therefore -- do not have chromosomes). Yet in natural development of the organism, a bunch of stem cells, which are of regular (diploid set of chromosomes) type, are evolving to form the ovaries, containing from very beginning all the ova (egg cells) that the female may have in her life. Ovum does only have a haploid¹ chromosomes set, until fertilization.

In their procedure the (full, diploid) genetic content of a "induced pluripotent stem cells" gets placed into an ovary-like culture of cells in order to make it ultimately evolve into an ovum. This evolution involves a "meiosis" type of cellular division, in which the end result are haploid cells, and the genetic load gets thinned out. Therefore, it will need fertilization -- a complementary chromosome set from another source.

What they don't talk about (but should) is telomeres², that normal cells, upon division, loose genetic material and thus -- degrade from reproductive point of view.

¹ https://en.wikipedia.org/wiki/Ploidy

² https://en.wikipedia.org/wiki/Telomere

No, I don’t think so, because the egg still needs to be fertilized by a sperm cell to develop into an embryo.

Now if the sperm cell were from the same donor I don’t know what would happen