What breed is Grumpy Cat?

Grumpy Cat is not a breed of cat. She is a random bred cat, a “moggie”. The record needs to be put straight because the PandaWhale website confidentially states that she is a “Snowshoe Siamese” (they mean “Snowshoe”). She is not. Sorry.
How do I know? Grumpy Cat’s owners say they are not sure what breed she is. That is a bad start because they are making the presumption that she is a breed of cat. However, pedigree, purebred cats are quite rare. Nearly all domestic cats are random bred (non-pedigree, non-purebred).
They say her mother is a domestic short hair calico cat. That implies non-pedigree. They go on to say that her father has grey and white stripes. Once again, there is no reference to a cat breed. I have not seen a picture of Grumpy’s father but he appears to be a bicolour coated cat and random bred. Update: thanks to Marc (see comment), I can see that her dad is a grey mackerel tabby and white moggie. The coat is slightly diluted.
Here is the family (thanks to Marc):

Grumpy Cat family tree
Grumpy Cat’s brother is Pokey (source: PandaWhale website). Pokey is a cute black and white cat. Pokey has all the appearance of a random bred cat (see header picture).
The pedigree (family tree) that I see on the internet strongly indicates that Grumpy Cat is a random bred cat and not a breed of cat. As for her appearance, yes, it is as if she is a dwarf cat and a Snowshoe cat.
However, her coat type (Siamese pointing with white fur within the pointing) is due to the presence of the pointing gene and the piebald gene (also called the “white spotting gene“). This does not mean she is a pedigree cat. To be a breed of a cat in the USA, a cat has to be registered with a cat association such as the Cat Fanciers’ Association (CFA). This is not the case. We would know if she was.
I discuss the Snowshoe cat on this page. I’ll quote a section about appearance:
The white spotting gene interacts with the Siamese gene and overlays on top of the pointing pushing out the dark pointing caused by the Siamese gene to produce the white markings on the face, limbs and front of the cat.
Grumpy’s appearance is simply about the presence of genes within her. The presence of these genes does not mean she is a breed of cat. The two are separate issues.
As for the dwarfism, this, too, is due to the presence of a gene. In this case a genetic mutation. The same gene has probably caused facial deformities which gives her that famous face.
There it is: Grumpy Cat has inherited certain genes by pure chance which have created her unique appearance but she is not a breed of cat.
Associated page: What breed is my cat?