I've been thinking of a method of classifying the level of duplication (actually, the level of difference) of two questions for a while. I'm not suggesting this as a site-wide standard or anything, I just think it helps to discuss exactly what the problem is.
Difference Level 0
This is just a special case. If two puzzles are exactly the same (ignoring punctuation, etc.), they're different at Level 0.
Difference Level 1
Two puzzles that are really the same puzzle in different clothing are different at Level 1. These are puzzles where the actual puzzle is the same, but the "fluff" text is different. That is, they're both the same problem, reasoning, and solution, but one is about aliens testing our species and the other is about a psychopath who wants to kill people who can't solve the puzzle.
Difference Level 2
Level 2 is about puzzles that are the same kind of puzzle, but have different parameters. For example, two different Sudoku puzzles are different at level 2. The solution to one puzzle is not the same as the solution to another (in more than a cosmetic sense), but the same techniques and rules apply to the puzzle.
Difference Level 3
Puzzles that differ at level 3 are alike in spirit, but really aren't the same type of puzzle. Consider a Sudoku puzzle and a "Jigsaw Sudoku" puzzle. There's clearly a lot in common, but there's a crucial variation that make the two varieties different. Your example with sugar cubes that fuse together is different at this level from the other two you mentioned.
Difference Level 4
Finally, level 4 involves puzzles whose types are completely different.
Notice that Levels 0-2 involve individual puzzles and 2-4 involve kinds of puzzles.
I think it's pretty agreeable that if two puzzles are different at levels 3 or 4, they shouldn't be considered duplicate. If they're level 0, they're obviously duplicate. The question seems to be asking specifically about level 1, but I think it's also worth talking about level 2.
Specifically, I think all puzzles that are different from another puzzle at level 1 or 2 should be marked duplicate. If we don't want Puzzling to turn into a glorified puzzle repository, we should disallow level 2 duplication. I think it's obvious that level 1 is too similar to allow on the site, but that also follows as a natural consequence of outlawing level 2 duplicates.
What do we do with interesting level 2 duplicates?
Especially when it comes to the recent chess questions, it seems like there's some interest in people seeing more of the same. It also feels a bit weird to have a single Sudoku puzzle; it's like that one represents them all, or something. We could consider making questions for types of puzzles as well. These could be about how to make such a puzzle, strategies for solving, and maybe finding more examples. Maybe this is a subject for another meta question, though.