Why was polyploidy not lethal in certain octodontid rodents?
Actually, that is not what is discussed in the question you linked to. The following is a quote from the very comprehensive accepted answer (emphasis mine):


  Polyploidy arises easily in both animals and plants, but reproductive
  strategies might prevent it from propagating in certain circumstances,
  rather than any reduction in fitness resulting from the genome
  duplication.


In fact, try rereading that answer and the references therein, it answers your general question.

There is a popular theory (mostly accepted) that there have been whole genome duplication events (WGDs) in the vertebrate ancestry. If true, it means that all mammals are the descendents of polyploid ancestors. For a very nice review of WGDs in vertebrate evolution, see here [1]. Octomys is simply the only known mammal with a more recent WGD event. As for what makes it special (taken from [2]):


  Our data demonstrate that parental-specific silencing of at least one
  gene and normal X chromosomal dosage mechanism are conserved in the
  tetraploid genome. We hypothesize a concerted action of genetic and
  epigenetic mechanisms during the process of functional diploidization
  of this tetraploid genome.


1) Van de Peer Y, Maere S, Meyer A., The evolutionary significance of ancient genome duplications., Nat Rev Genet. 2009 Oct;10(10):725-32. 

2) Bacquet C, et al., Epigenetic processes in a tetraploid mammal, Mamm Genome. 2008 Jun;19(6):439-47.