There is no issue number for this. It turned up when I was checking another bug, but was unrelated to it. You are supposed to be able to use
MathJax.InputJax.TeX.Environment(name,prefix,suffix,n,default)
(after loading the TeX newcommand extension) in order to define a new command, where prefix is the TeX code to insert at the beginning of the environment, suffix is the TeX to insert at the end, n is the number of arguments required for the environment, and default is the default for the argument. The n and default are not required.
This works as advertised, except for one thing: if the prefix includes a \begin{...} and the suffix includes an \end{...}, MathJax issues an error about the nesting being wrong. With this fix, the begin and end work properly. E.g.,
MathJax.InputJax.TeX.Environment("nested","\\begin{matrix}","\\end{matrix}");would cause \begin{nested} a& b \end{nested} to produce the message '\begin{matrix} ended by \end{nested}` without the patch. With the patch, you should get a matrix as expected.