I propose a tag variant which I think is important, but this is a special tag which cannot stand alone. This tag means the variant of another tag.
If we create a puzzle like solving a modified horse step on chessboard, I think it quite misleading if we put the tag chess, but it is not if we put 2 tags chess and variant.
I checked the tags, and there are many that can be put together with the proposed variant tag. For example, chess, sudoku, rubiks-cube, dice, matches, dominoes, tic-tac-toe, scrabble, etc.
I have created a sudoku-like puzzle, and I put the tag sudoku. But my friend says it is not sudoku, so I should not put the tag sudoku.