There do seem to be a lot of games of that type, implemented using various technologies (Flash, HTML, etc.). I looked around a bit and couldn't find any clear answers, but I wonder if perhaps this is generally done using 2-d graphics with large sprite sheets used for the ball animations.
Here are a couple threads that touch on the topic:
1
2
The first thread includes an example of what such a sprite sheet might look like.
In some of the games I checked I saw some hints that the graphics might be 2-d, such as a little quantization in the rolling, and sunk balls just fading out rather than behaving in a natural 3-d manner. Also, if the graphics are 3-d, that would be some very nice rendering for e.g. an HTML or Flash game.
So I don't know the answer for sure, but I suspect the graphics are 2-d and sprite-based. Maybe someone else knows and can jump in.