Is there an accepted name for Ross Quinlan's adaptation of the ID3 decision algorithm to use a Pearson's chi-squared test for independence?
Unfortunately, I'm not able to get into detail of the ID3 paper you cited.

I read the Quinlan's book about C4.5 and I don't remember any quote about Chi-square splitting procedure. However, it exists a decision trees induction process that uses Chi-squares as splitting procedure, it is CHAID: http://en.wikipedia.org/wiki/CHAID.

By the way, do you really need a Chi-square splitting procedure? Good permances of C4.5 are well known, and it uses Information Gain as splitting criterion. Moreover, classical Data Mining books (such as Introduction to Data Mining by Tan et al.) state that better performances can be achieved with different pruning techniques rather than different splitting criteria. 

If you really want a Chi-square splitting procedure I would suggest to use CHAID or modify the Java implementation of C4.5 in WEKA.