The RandomSortField type doesn't hold any data, so you don't need to define any column in your database to go into it.
When you query your data, you'll add "sort=random_<seed>" to the query parameters, where you define some value (whatever you want) for the <seed>. If you issue the same query later with the same seed value, you should get the same results (assuming you haven't indexed new data).
Note the field type definition in the example is not complete. It should be: