In researching this further, we found out that the best way to get that information, is by getting the values from the Quote Close activity entity (quoteclose). The Quote Close entity is basically an Activity entity, so it has the Actual Start Date and Actual End Date fields. The Actual End Date field that is displayed to us is basically the Quote won field.
In order to display the information of the Quote including closure information in a view, we would need to query the Activity Entity, and add a Join to the Regarding (Quote) relationship. Thie would allow us to query the Quote Closure information (as seen in the screenshot below).
If we need to see the columns from the Quote Closure entity as well, we can Add Columns, and change the record type from Activity to Regarding (Quote):