Unfortunately, this depiction contain some truth but a lot that misleads. In the case of the "Well" the reason it seems to work is because there is the gravitational force of the earth which pulls things down the well. Of course if you are describing gravity around the earth, this does not work. But there is a germ of an idea there, because space around the earth actually is deformed into something very roughly like the geometry of those wells. The reason why is that the circumference of circles is less than 2 pi times the radius of the circle - as it is in those well models. In other words, the distance through the earth is larger by about one millionth of a percent (about a centimeter) than the circumference of the earth divided by 2 pi. However, except for things moving near the speed of light, the effect of this spatial curvature is negligible in determining the path that a particle follows. For light it is this spatial curvature which makes the deflection of light past say the sun be twice what you would naively calculate, and which Einstein calculated in 1908 before he had developed his theory of General Relativity. But for normally moving particles, the effect of this spatial curvature is very very small. The main effect of gravity as described in Einstein's theory has to do with time, and the relation of paths through time. One way of encoding this is to say that gravity is the unequal flow of time from place to place. However this feature of GR is very difficult to make some simple model , so those who simplify things overmuch tend to "cheat" by pretending that gravity has something to do with spatial curvature (á la the well).
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