What type is this sorting algorithm?
This is known as counting sort. On a domain of size $d$, counting sort runs in time $O(dn)$, compared to $O(n\log n)$ of comparison-based sorts. When $d\ll\log n$, i.e., when the domain is small compared to the total number of elements, we would expect counting sort to be faster. Counting sort can even be iterated, and this is known as radix sort.

If $d = o(\log n)$, then counting sort runs in time $o(n\log n)$, which might seem to contradict the well-known $\Omega(n\log n)$ lower bound on sorting. There is no contradiction, however, since the lower bound only holds for comparison-based sorts, which counting sort evidently isn't.