Making TikZ nodes hyperlinkable

Here's a new TikZ style called hyperlink node=<target> that takes a hypertarget reference. It works by measuring the node it is supplied to, and then placing a new invisible node on top of that. The new node has the content \hyperlink{<target>}{\phantom{\rule{<width of node>}{<height of node>}}, so it has the same size as the original node, but the whole area is clickable.

\documentclass{article}
\usepackage[hidelinks]{hyperref}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\tikzset{
    hyperlink node/.style={
        alias=sourcenode,
        append after command={
            let     \p1 = (sourcenode.north west),
                \p2=(sourcenode.south east),
                \n1={\x2-\x1},
                \n2={\y1-\y2} in
            node [inner sep=0pt, outer sep=0pt,anchor=north west,at=(\p1)] {\hyperlink{#1}{\XeTeXLinkBox{\phantom{\rule{\n1}{\n2}}}}}
                    %xelatex needs \XeTeXLinkBox, won't create a link unless it
                    %finds text --- rules don't work without \XeTeXLinkBox.
                    %Still builds correctly with pdflatex and lualatex
        }
    }
}

\tikz \node [draw, inner sep=2ex,hyperlink node=pagetwo] {Go to Page Two};

\clearpage
\hypertarget{pagetwo}{Page Two}
\end{document} 

Apart from Jake's nice idea – here's some code that works fine here in a recent document using the code from Drawing a directory listing a la the tree command in TikZ (answer of A. Stacey) and your MWE. It's not as fancy as your's, but maybe stylish, too.

\documentclass{article} 

\usepackage{tikz}
%------------------%
\makeatletter
\newcount\dirtree@lvl
\newcount\dirtree@plvl
\newcount\dirtree@clvl
\def\dirtree@growth{%
  \ifnum\tikznumberofcurrentchild=1\relax
  \global\advance\dirtree@plvl by 1
  \expandafter\xdef\csname dirtree@p@\the\dirtree@plvl\endcsname{\the\dirtree@lvl}
  \fi
  \global\advance\dirtree@lvl by 1\relax
  \dirtree@clvl=\dirtree@lvl
  \advance\dirtree@clvl by -\csname dirtree@p@\the\dirtree@plvl\endcsname
  \pgf@xa=0.5cm\relax % change the length to your needs
  \pgf@ya=-0.75cm\relax % change the length to your needs
  \pgf@ya=\dirtree@clvl\pgf@ya
  \pgftransformshift{\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
  \ifnum\tikznumberofcurrentchild=\tikznumberofchildren
  \global\advance\dirtree@plvl by -1
  \fi
}
\tikzset{ %definition of a new style "dirtree"
  dirtree/.style={
    growth function=\dirtree@growth,
    every node/.style={anchor=north},
    every child node/.style={anchor=west},
    edge from parent path={(\tikzparentnode\tikzparentanchor) |- (\tikzchildnode\tikzchildanchor)}
  }
}
\makeatother
%------------------%

\usepackage{hyperref}

\begin{document}

\begin{tikzpicture}[dirtree] % it's what we defined above

\node {\textbf{COOL TOC}}
    child { node {\hyperref[install]{installation} }
        child { node {\hyperref[linux]{Linux}} }
        child { node {\hyperref[mac]{Mac}} }
        child { node {\hyperref[win]{Windows}} }
    }
    child {node {\hyperref[start]{Get Started}}
        child { node {\hyperref[caseA]{do A}} }
        child { node {\hyperref[caseB]{do B}} }
    }
    child {node {\hyperref[trbl-shoot]{troubleshoot}}
        child {node {\hyperref[caseX]{if X happens}}}
        child {node {\hyperref[caseY]{if Y happens}}}
    }
    % I've put the external resources to the end:
    child {node {Looking Further}
        child { node {\href{file:manual.pdf}{manual}} }% works only, if "manual.pdf" is in
                                                       % the same directory as the compiled
                                                       % version of this document
        child { node {\href{http://website.example.com/online-resource/}{online}} }
    };
\end{tikzpicture}

\section*{Installation}\label{install}
\subsection*{Linux}\label{linux}
Some content.

\subsection*{Mac}\label{mac}
Some content.

\subsection*{Windows}\label{win}
Some content.

\section*{Get started}\label{start}
\subsection*{First: Do A}\label{caseA}
Some content.

\subsection*{Second: Do B}\label{caseB}
 Some content.

\section*{Trouble shooting}\label{trbl-shoot}
\subsection*{If X happens:}\label{caseX}
Some content.

\subsection*{If Y happens:}\label{caseY}
 Some content.

 \end{document}