My definition of a roguelike

I consider whether a game is roguelike on two axes:

Even if a game is strictly not mechanically rogulike, it may be highly prototypically roguelike.
A game, here, may be a particular configuration of a game, or a game played in a specific manner, or a specific part of a game.

Being mechanically roguelike

There are three strict criteria for being mechanically roguelike. Failing to meet them excludes a game from being mechanically roguelike.

It is possible to classify a game differently depending on how runs are defined. Often, there is a natural or common notion of runs that is most readily identified, but sometimes, an interesting different classification is reached by redefining a run.
Here, gameplay is taken to allow for repeated initializations of the game, and interruption or suspension of the game. Perspectives may also differ in how gameplay is delimited.

There are two criteria that determine the degree to which a game is mechanically roguelike, if it satisfies the above strict criteria.

Being prototypically roguelike

Being prototypically roguelike is an amalgamation of yet more axes. Here I list named stages per axis in order from most prototypically roguelike to least. All criteria are more relevant as they apply to the runs (should the game be mechanically roguelike).