Interesting; \centerdot does seem to be a misnomer, doesn't it? The MathJax fonts contains the proper character, but I don't see an appropriate version in the STIX fonts. So while you could get it to work with the MathJax web fonts, it would fail with people using STIX.
So perhaps the following would work for you:
\def\centerdot{\mathbin{\Rule{.2em}{.2em}{0px}}}
which makes a binary operator from a small black square. You can include this in your configuration as follows:
<script type="text/x-mathjax-config">
MathJax.Hub.Config){
TeX: {
Macros: {
centerdot: "\\mathbin{\\Rule{.2em}{.2em}{0px}}"
}
}
});
</script>
Place this BEFORE the script that loads MathJax.js itself.
Davide