SCPM: The game was made in Adobe AIR, and it seems GOG Galaxy SDK doesn't have support for it, so there's no Galaxy achievements. It looks like the dev did try to implement it before figuring out it didn't work:
https://www.exophase.com/game/the-elephant-collection-gog/achievements/
Thanks for the info...
I thought this was discontinued but a quick search showed that AIR found a new home. I can totally understand why they choose that to "remaster" Flash games and also why it may not be supported by GOG (due to the limited, at least as far as I know, relevance of AIR).
If someone more technically minded than I am when it comes to achievements support, I'd be curious to know why it Steam supports it and not GOG. Is Steam SDK, by design, more technology agnostic or is it just a matter of resources and Steam having more people working on it allowing more technologies to be supported?