This is caused by the lack of either playerprofiles8.lsf or LevelCache folder in the %appdata% folder, which contain records of your character in the world. Not sure which one exactly, most likely the profile one, but these are not uploaded to the cloud. So if you reinstall Windows or in your case move to another system then these files do not transfer over.
I just checked those files/folders on my own pc and they are both present but as of today I have THREE traveller's chests. One for each hotfix?
I've played on one pc, I reinstalled once between chest 2 and 3 for unrelated reasons, but the reinstall didn't change anything, in case anyone wonders.
Edit: it might be related to different camp sites! I remember camping at a cave camp and missing a chest there alltogether before resting, after rest a chest was there and after that I noticed an extra chest in camp. Today I rested at the Underdark camp for the first time and that's where the third chest appeared.
