In this specific case, I have permission from the publisher to implement the game, as long as I put in the appropriate trademark notices and don't use the original graphics.

I got that permission in a bit of a roundabout way though. The system didn't start off as a full implementation of the game but just as a tool for making it a little bit easier to manually moderate a play-by-email/play-by-forum games, and the publisher was clearly implicitly ok with (in fact one of the first uses of the tool was for an exhibition match of sorts with one of the designers of the game). Once it became clear that this had slowly morphed into a full implementation of the game, I asked for formal permission and exactly where the limits were (e.g. on the graphics). So there was a bit more "asking for forgiveness rather than permission" involved than I'm really comfortable with. In general you should always ask up front.

This area is a bit of an interesting balancing act for the publishers of hobby board games. On one hand it's almost certain that a free online implementation gives the game a lot more longevity and thus drives long-term sales. It means the game continues to be played a lot more by the existing players, which means they continue discussing it. This in turn attracts new players to the game, and sells more physical copies. It also means that people are excited for any new expansions, since they've played the base game enough to want the variety.

On the other hand free online implementations do probably make it harder to license the game for a commercial digital implementation. For example tablet implementations of board games looked like a big deal a few years ago. But my feeling is that it didn't actually turn out to be a viable business in the long run. Making the tablet implementations is just too expensive and outside of a handful of games with massive pre-existing mass market appeal (talking of the Carcassonne / Ticket to Ride tier of games) the sales just aren't there.

As far as I know (IANAL) only the art and possibly the exact wording of things on cards can be protected. The actual game mechanisms can not. Magic the Gathering famously had (iirc. it expired in 2014) a patent on tapping (turning a card sideways) but you could still use that mechanism without calling it tapping (or using the tap-icon).

Basically you can clone any game if you remove all the flavour. The more you add, the dicier it may become. So having red, green and blue cards should be trivially ok. Naming the gnomes, dwarfs and humans should also be ok. more detail than that and it's thin ice.

Would love actual experience. I'm sort of cloning a board game as well (for personal use and AI research).

Love Terra Mystica, probably played on OP's site before buying the game :)