The glossary-superragged style reserves 0.6\hsize for the description text. Using enumitem we can set the label width to 0.4\hsize and indent the description this far, as follows:

\documentclass{article}
\usepackage{enumitem}
\usepackage{etoolbox}
\let\bulletdescriptionlabel\descriptionlabel
\patchcmd\bulletdescriptionlabel
{#1}
{{\normalfont\textbullet\ }#1\hfil}
{}{}
\newlist{mydescription}{description}{1}
\setlist[mydescription]
{before=\let\makelabel\bulletdescriptionlabel,leftmargin=0.4\hsize,labelindent=0em,itemindent=!,labelwidth=!}
\begin{document}
\begin{mydescription}
\item[First heading] A description text that is long enough to
spread on to the next line, and saying absolutely nothing.
\item[Second heading] A description text that is long enough to
spread on to the next line, and saying absolutely nothing.
\item[Third rather longer heading] A description text that is long enough to
spread on to the next line, and saying absolutely nothing.
\end{mydescription}
\end{document}
This builds on @egreg's last solution in the question you link to (https://tex.stackexchange.com/a/60282/15925). A final \hfil has been added to the labels to make them left-aligned. The main indentation is acheived by setting leftmarigin to 0.4\hsize and labelindent to zero. The remaining parameters are computed by enumitem via the ! options, so that labelwidth+labelsep equals our leftmargin.