Connect N type games seem almost certain to exist elsewhere, as are connection games such as Hex. The fundamental concept is very basic, and the there are not a lot of variations.
There are a plethora of abstract games that have been invented that are not played very much, but seem to have the potential for extreme depth of play. I would be willing to bet that some of those neglected games are played by Aliens somewhere in the Universe, and enjoy the level of success in their society that Chess or Go enjoy here.
This is a great thought. Do you know if anyone is looking at computationally examining these overlooked games and trying to find the ones with truly excellent depth, so that they may get greater attention? That sounds like a fun project.
I think the game Quoridor has simple rules but is very deep. It's a 9x9 grid of cells where one places length-2 walls between the cells to inhibit movement (the goal is to get your piece to the opposite side of the board).
On your turn you can either move your piece, or place a wall. You have 10 walls to place.
The one non-obvious rule that completely changes the strategy of the game is that you cannot make it impossible for the other player to win (you can't simply box them in).
So a common theme is to try to maximize the amount of paths your opponent has while minimizing the number of paths you have, so that whenever your opponent commits to a path, you block it and force them to backtrack.
But say your opponent has 2 paths, and they begin to commit to one. You are waiting for them to commit further so you can block it and force them to backtrack. But before you do it, they block the other path themselves. Now it is illegal for you to block their only remaining path.
On the face of it, the branching factor is much higher than chess. On each turn one has 100+ possible moves. I have written pretty highly optimized minimax AB-pruning type AIs for it and have never managed to make an AI that can search deeper than 7 moves or so in a reasonable amount of time, and my AI was the strongest (by far) of any I could find online (and better than any human player in my friend group).
It's pretty computationally difficult due to the "cannot make it impossible to win" rule. If you do it naively, that involves an A-star search for each possible move. You'll max out around 4 moves deep with that strategy. A few observations will get you a bit higher. e.g. A wall cannot possibly block a path unless both ends of the wall touch another wall (or edge of board).
There might be some sophisticated graph cutting algorithms I am not aware of that could make this tractable, but I haven't found any that mapped too well onto the problem.
I think Quoridor is actually really ripe for an AlphaZero type approach (due to the high branching factor and expensive compute needed to determine move legality), and I would love to see a superhuman game played.
There are a plethora of abstract games that have been invented that are not played very much, but seem to have the potential for extreme depth of play. I would be willing to bet that some of those neglected games are played by Aliens somewhere in the Universe, and enjoy the level of success in their society that Chess or Go enjoy here.