In vertebrates, cyclopia is caused by a trisomy. In humans for example it is the 13, sometimes the 4. I have seen it in cats also, and one case has been reported in sharks.
Do not google for it if you are sensitive to images of deformed, stillborn babies.
Also, for those who don't know what trisomy means: it's when you have one extra copy of a chromosome.
Now let's supoose that, due to chance, a mutation happens where some specimens have not trisomy, but tetrasomy, and they somehow survive and breed.
Supoose that a gene, or set of genes, in the affected chromosome significantly increases survivability, and having multiple copies helps even further. Natural selection would favor the tetrasomic and they would eventually give rise to a new species.
If this set of genes gives more chances of survival and breeding than having two eyes instead of one, then having only one eye is just a small price to pay.
Such tetrasomy may also explain the cyclops' great size and strength. Perhaps in their environment those were the factors that helped them survive.