Bags are either checked or not. This bag was checked. Carriers may used different marketing terms, but those terms are of no consequence.

The Montreal Convention sets maximum compensation at fair market value up to roughly EUR 1430 per passenger and did so back in 1984.

Most bags which go missing on short-hauls where the path they take is very limited are found in short order or were outright stolen.

As you aren't missing anything essential, I would simply sit back and wait for the process to take it's course so long as BA has your parents local contact information. If that changes, be sure to let BA know, so that the bag can be delivered to the new location.