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The problem with those variants is that they force the usual chess pieces in contexts where they don't really belong.

Rooks and bishops follow the obvious geometry of the square chessboard. Knights are the natural complement of rooks and bishops: they move to any of the closest squares neither a rook nor a bishop could reach.

Pawns defend each other and form the game's "structure".

Queens are rather arbitrary (you could have rook+knight or bishop+knight instead of rook+bishop), but a strong piece is needed to allow for dynamic play.

On an hexagon they don't really make sense. Is there a more "natural" set of pieces that's built on the geometry of an hexagon rather than being an awkward translation of the usual chess pieces?

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Not specifically "hexagonal chess, but a very tactically similar hexagonal abstract strategy game called "Hive"[1] is very well regarded in the board game community and relevant to this discussion for anybody even tangentially interested.

Personally, I think it's more worth spending your time looking into that than yet another variant of chess. Also if you get a hankering to play it, it is available on boardgamearena online.

[1] https://boardgamegeek.com/boardgame/2655/hive

Hive is fantastic fun. I found it easy to learn, but that there was some strategic depth that really gave it replay value. An interesting aspect is that there isn't a board as such, rather the pieces together constitute the playing area which morphs as the game unfolds. It's a great on-the-go game since the pieces are tough and it's a convenient size to be chucked in a bag for the beach, train journeys, etc.

The moves described in the video seemed like they were decent analogues to me. The bishop moved along the same color and could attack rooks and knights from safety and could slide between pieces. Rooks could attack bishops and knights safely. Knights could attack rooks and bishops and queens safely.

What specifically did you think was way out of context?

If you watch the video, you'll find that on a hexagon, things make no less sense than on a grid and the folks who worked out hexagonal chess actually did a pretty great job preserving all those roles. Your brain just isn't use to hexagon logic.

I think it would be cool if the base of the chess piece was a triangle instead of a circle and orientation mattered. So you could introduce a new move into the game which is picking up a piece and twisting it 60 degrees to put you on a different axis of the hexagon. This opens up three new directions (sides 2, 4, and 6) and closes the previous three (sides 1, 2, and 3).

Edit: Fix math.

You'd twist it 60 degrees, not 120 degrees, right?

Yep!!! Haha. Fixed, thank you.

You should look into Khet (commonly described as "laser chess")

I find it kind of hilarious that whites first move can be 1. Qb4, past their beginning pawn wall, and staring right that blacks queen through blacks pawn wall, and where it is immediately taken by black’s first move: 1... Qxb4

Did you even watch the video?

Rooks having 3 directions in hexagonal chess is "as naturally built on the geometry of a hexagon", as rooks having 2 directions in square chess. I have no idea what you're objecting to.

You entirely miss the playfullness that is inherent in chess variants. You switch up the rules and see what happens.

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