Discretization in general means to split a while into discrete parts. Discrete parts refers to the notion that they have a size -- as opposed to differential parts which do not have a finite size in math.
Often, people use discretizing space to refer to splitting the region into a regular grid which can be indexed in 2d or 3d.
In this paper it appears that each discretization's behavior is evaluated independently of what is around it. In the picture, the pipe is considered as a pipe and its functionality is tested without regard to what is around it. Only the player and the pipe would be tested without regards to the coins or other platforms.
My 2 cents.
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He may have had something like movement in mind. In discrete space and time, the player would move from one grid square to the next in "turns." Each turn can be thought of as a span of time. This idea of playing the game with turns helps create the logic required to move the character and interact with the environment.
This seems to be a very abstract, high level presentation.