This is a classic instance of one of my favourite evolutionary phenomena with the unfortunate, clumsy names, "meiotic drive" and "segregation distortion". The reason drive is so compelling is that it is the archetypal result of selfish genes in action, and the perfect example to trot out when explaining that selection does not act "for the good of the species", or sometimes, for the good of the individual.
From the viewpoint of a driving allele (a particular version of a gene) on the X chromosome, genes on the Y chromosome are a waste of space. A good way to double its fitness, would be to make sure none of the Y chromosomes get into sperm, so all the offspring of a male with this driving allele will be daughters (because he would only make sperm with X chromosomes). This is no good for the Y chromosome, and it seems to have solved the problem by acquiring genes that resemble the driving X copies enough to suppress them. An arms race of more driving X copies and more defending Y ensues.
The other cost of a driving allele, whether it is on the X or some other chromosome, is that the male carrying this allele will be making much less sperm than males without the rogue gene. Essentially, his sperm making efficiency is being compromised by these selfish genes because sperm that don't carry them don't make it to the next generation.
If all males had exclusive access to their mates, this wouldn't be much of a problem, since even half their sperm would be more than enough to fertilise eggs. However, most female mice are likely to mate with more than one male, so sperm competition would select for males without driving alleles because they would have more sperm than males handicapped by internal genomic conflicts.
One prediction that arises from this, is that one should see more signs of an arms race between genes on the X and Y chromosomes in species with less sperm competition. In other words, more repeated copies of the driver and suppressor alleles on both sex chromosomes -- a phenomenon known as co-amplification. The sex chromosomes of three mouse species in the Y chromosome paper do indeed vary in composition and size, but it isn't clear how much sperm competition varies in these species. Furthermore, mating systems are notoriously variable and evolve rapidly, so they might not generate a steady enough selection pressure to detect clear differences in co-amplification between conflicting sex chromosomes.
Soh, Y. Q. S., Alföldi, J., Pyntikova, T., Brown, L. G., Graves, T., Minx, P. J., … Page, D. C. (2014). Sequencing the Mouse Y Chromosome Reveals Convergent Gene Acquisition and Amplification on Both Sex Chromosomes. Cell, 159(4), 800–813. doi:10.1016/j.cell.2014.09.052