Line-spacing in a cell of table

\arraystretch only affects line spacing between table rows. In an X column, you can change the spacing between lines inside a cell by adjusting \baselineskip. Below is the same example coded in two slightly different ways, the first using \ctable, the other using your tabularx set-up. Notice the \ctable gives better spacing for the caption relative to the table.

\documentclass[10pt]{article}

\usepackage{ctable}

\begin{document}

{\renewcommand{\arraystretch}{1.5}
\ctable[caption = Test,pos=htp,width=\textwidth]
{c l >{\setlength{\baselineskip}{1.5\baselineskip}}X}{}{
\FL
No. & Code  & Name                                \ML[0.08em]
01  & 01XXX & Agriculture, forestry and fishing   \NN
02  & 05XXX & Manufacture of Electronic Components, Computer, 
Radio, Television and Communication Equipment and Apparatuses
\NN
03  & 06XXX & Nursing                             \LL
}}

\begin{table}[htp]
  \renewcommand{\arraystretch}{1.5}
  \caption{Test}
  \begin{tabularx}{\textwidth}{c l >{\setlength{\baselineskip}{1.5\baselineskip}}X}
    \FL
    No. & Code  & Name                                \ML[0.08em]
    01  & 01XXX & Agriculture, forestry and fishing   \NN
    02  & 05XXX & Manufacture of Electronic Components, Computer, 
    Radio, Television and Communication Equipment and Apparatuses
    \NN
    03  & 06XXX & Nursing                             \LL
  \end{tabularx}
  \label{tab:test}
\end{table}

\end{document}

I demonstrated this with increasing the spacing, as this is more realistic. Squeezing will work too, just replace both 1.5 by 0.75 in the \arraystretch and the >{...}X, but it does not look too good. As Mico suggests, in such situations reducing font sizes is better. In both cases, note that the change to \arraystretch has been inside a group/environment, to prevent this affecting other places later in the document.