How does projecting a few IR dots capture an image three dimensionally?
The projected differaction pattern (formed out of Gaussians) has a special assymetric structure, which in turn would help the software resolve the stereo correspondence problem. After correspondence is obtained, the distance can be triangulated, as in a simple stereo setting.

For further info, please check the PrimeSense patent:
http://www.google.com/patents/US20090185274

Other stereo reconstruction techniques might use color coded patterns, blue light patterns, phase shifting projections and so on. Generally, tools projecting fewer dots enjoy muliple pattern projection and encode every pattern differently. This might for example obtained by rotating the projector or programming it to project different light stripes.

Depending on the object to be reconstructed, using multiple cameras might just be enough as the RGB image information might provide you enough data to disambiguate. In this case, you wouldn't even have to project a pattern. 

The technique is generally called structured light and for further info you might check:
http://fofi.pagesperso-orange.fr/Downloads/Fofi_EI2004.pdf
http://eia.udg.es/~qsalvi/Tutorial_Coded_Light_Projection_Techniques_archivos/v3_document.html
http://en.wikipedia.org/wiki/Structured_light