If you are looking at this Title ID from a technical or archival perspective, "working" usually refers to the software's stability: Version 1.0.0 and Beyond
Beyond technical "work," the HD-2D Remake adds several modern features to the core game: Dragon Quest III HD-2D's Free Switch 2 Upgrade is Brilliant dragon quest iii hd2d remake 01003e601e324000 work
Signature patches (sigpatches) allow your custom firmware to recognize and launch installed backup games. If you are looking at this Title ID
These change with patches; verify via hex compare before/after a level-up. conversion is possible.
One advanced "work" for 01003E601E324000 is cross-platform save conversion. The Steam version uses a different save structure, but thanks to the HD-2D engine’s similarities, conversion is possible.