You are right that MathJax doesn't currently support \multicolumn or \cline. Because MathJax converts your TeX to MathML internally, support for \multicolumn would require the implementation of MathML's columnspan and rowspan attributes for the <mtd> element; these are not yet implemented (they complicate the layout algorithm considerably). The \cline macro is also a bit tricky, since MathML only has support for lines that go across the complete table.
It would be possible to use style attributes on the <mtd> elements to add borders to create shorter lines (at least in the CommonHTML output), but you don't have direct access to the underlying MathML from within TeX, so it would have to be done indirectly, and it would rely on knowing the internal workings of how the CommonHTML output is laid out. For example, setting the style
.mjx-mtable.titled > .mjx-table > .mjx-mtr:first-child > .mjx-mtd:first-child {
border-color: transparent ! important;
}
and then use
\class{titled}{
\begin{array}{r|cc}
& 1 & 2\\
\hline
10 & 50 & 60\\
1 & 100 & 300
\end{array}}
to get the lines like you asked for.
To get the full table takes a bit more work:
.mjx-mtable.titled-labeled > .mjx-table > .mjx-mtr:first-child > .mjx-mtd:nth-child(2),
.mjx-mtable.titled-labeled > .mjx-table > .mjx-mtr:nth-child(2) > .mjx-mtd:nth-child(2),
.mjx-mtable.titled-labeled > .mjx-table > .mjx-mtr:nth-child(2) > .mjx-mtd:first-child {
border-color: transparent ! important;
}
with
\class{titled-labeled}{\begin{array}{rr|rrrrr}
&&&&\hspace{-1.5em}\text{Demands}\hpace{-1.25em}\\
&100&100&100&100&100&100\\
\text{Supplies}&100&100&100&100&100&100\\
Here we use \hspace commands to hide the width of the top label, and the CSS removes the borders from the needed cells to get the lines you are looking for. Remember, this requires the CommonHTML output, because it is the one that uses CSS borders to produce the lines in the array. If the user switches to one of the other formats, the full lines will show.
Of course, this is a terrible hack. The real problem, here, is that table really isn't mathematics at all, and so you are using math to do something that should really be part of the page layout in HTML, not math. You have to do this sort of thing in LaTeX, because everything is done through TeX commands, but in web pages, you have HTML to do the page layout, and MathJax should only be used for the mathematics itself. So the way MathJax expects you to do this sort of thing is to use HTML tables with individual MathJax expressions inside the table cells (if needed).
Davide