From what I have understood by watching his TED talk, the algorithm he designed seems very similar to papers published in the NLP field recently [1] [2] [3]. I find it quite elegant, and I agree that the kid is really smart.

The idea behind those algorithms is to build a graph on words, using WordNet, or a corpus such as Wikipedia. Edges are added between words which are semantically close, or which often appear in the same documents. Then, to compare two words (or two bags of words), you compute the limiting distributions of the two random walks starting at each of the words. Those random walks will more explore nodes which are close to the starting nodes, and so, similar words will have similar random walks.

[1] Hughes, T. and Ramage, D. 2007. Lexical semantic relatedness with random graph walks ( http://acl.ldc.upenn.edu/D/D07/D07-1061.pdf )

[2] Ramage, D. and Rafferty, A.N. and Manning, C.D. 2009. Random walks for text semantic similarity ( http://nlp.stanford.edu/pubs/wordwalk-textgraphs09.pdf )

[3] Yeh, E. and Ramage, D. and Manning, C.D. and Agirre, E. and Soroa, A.. 2009. WikiWalk: random walks on Wikipedia for semantic relatedness ( http://nlp.stanford.edu/pubs/wikiwalk-textgraphs09.pdf )

[Update] Added the third reference.