On FICS (and in XBoard) this is the difference between the variants Giveaway and Suicide Chess. The first case you quote would not be for Giveaway but for Suicide. FICS also supports a third variant of this type: Losers Chess. There the checking rule applies, you win by being checkmated or bared, and stalemate is a draw.
I think the confusion in this article comes from the misconception that Losing Chess is a single variant. But it is not; it is a family, while Giveaway is a specific member of that family.
Note that being annihilated is a special case of stalemate: when you have no pieces you have no moves. Even in the case of Giveaway (your 3rd case) this means you have won, as no pieces will always be the lowest number of pieces. Rule options 1 and 3 are thus consistent; 2 is a strange exception, distinguishing some stalemates from others. In Losers Chess the primary goal is not stalemate but getting bared. Being checkmated is rare, and can usually not be forced.
On FICS (and in XBoard) this is the difference between the variants Giveaway and Suicide Chess. The first case you quote would not be for Giveaway but for Suicide. FICS also supports a third variant of this type: Losers Chess. There the checking rule applies, you win by being checkmated or bared, and stalemate is a draw.
I think the confusion in this article comes from the misconception that Losing Chess is a single variant. But it is not; it is a family, while Giveaway is a specific member of that family.
Note that being annihilated is a special case of stalemate: when you have no pieces you have no moves. Even in the case of Giveaway (your 3rd case) this means you have won, as no pieces will always be the lowest number of pieces. Rule options 1 and 3 are thus consistent; 2 is a strange exception, distinguishing some stalemates from others. In Losers Chess the primary goal is not stalemate but getting bared. Being checkmated is rare, and can usually not be forced.