In my head
sorting
Is really just ordering. There's no inherent requirement that the ordering in particular be well-defined, ascending/descending, or aesthetically pleasing.
M-W definition 3
the act of separating things and putting them in a particular order : the act of sorting things
A random order doesn't seem to break these definitions.
Let me expand my answer taking in the comments below and getting vaguely rigorous. No need to continue if you've been convinced.
A collection may be stated as
Collection = { x1, x2, ... , xn }
An order is a function that goes from N -> N where N is a natural number 1..n.
For a collection to be ordered that just means I can generate a list
(x1, 1)
(x2, 2)
(x3, 3)
Where the left hand side is the item and the right hand side is the position.
An order function just transforms positions. A random ordering might be
f:
1 -> 3
2 -> 1
3 -> 2
I would apply that order function to get a new ordering out. I have successfully separated things and put them in a particular order. The new collection is still ordered, it's just been sorted into a different one.
Vaguely philosophical addendum
The idea of sorting has to be this vague because you aren't limited to sorting items lexicographically or numerically. Let's say I want to sort a set of countries. The countries themselves cannot be ordered meaningfully but I can define an ordering based on items that I know how to order. I can do it by population, or by area, or any number of other metrics. I also might be able to do it by ratio of people to cattle or any number of arbitrary functions. Because the potential orderings are so arbitrary all we can really say about them is that they are orderings. You'll have a bugger of a time trying to define rules for ordering that capture all potential valid cases. After all, it's perfectly valid for me to say that I'm going to sort this list of countries based on how happy they make me. These countries are now being judged on something that's outside the system where the system is the list. In a similar way, your random ordering is being sorted by something that's outside the system where the system is the list. In the case of the random sort, it's likely truly being ordered on a function of the system time.