Okay. I didn't pay attention to your code, you're using SALV, my answer was for pure ALV grid. I'll try for SALV. SAP doesn't allow editing in SALV (while it's allowed but not supported for ALV grid), except if you use some workarounds. Anyway, I'll try to make it work for SALV and revert soon.
For set_cell_type_column, you must make sure cellstyles is of type SALV_T_INT4_COLUMN, so that to define its type (checkbox, hotspot, ...) There's also type checkbox_hotspot, I wonder whether this type allows the handling of editable checkboxes...