Those examples in moodle docs are written for mimetex and they work with cgi mimetex without problems - for example http://www.imathas.com/cgi-bin/mimetex.cgi?\circle(150) used in img tag (see insert image button in editor toolbar)
<img src="http://www.imathas.com/cgi-bin/mimetex.cgi?\circle(150)" alt="Circle" width="152" height="150" />
If your tex filter was using mimetex and you had removed \line from blacklisted words array - see http://moodle.org/mod/forum/discuss.php?d=209285 - also your tex filter could output the examples with mimetex.
However mimetex can't use any usepackage commands so if your site is using texlive etc you need to check first which kind of commands different extra packages use - "picture", "xy", "pstricks", "graphicx"... - and those packages do not understand the "language" of these mimetex examples.
Finally pure tex renderers like mathJax do not have these commands at all.