Any shorter code for drawing this in tikz?

I don't know much about graphs so I won't attempt to use the graph libraries but you can renumber your nodes bit more meaningfully and then do a typical adjacency matrix approach.

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.markings, arrows}
\begin{document}    
\begin{tikzpicture}[mdar/.style={
    decoration={markings, mark=at position 0.45 with {\arrow{stealth}}},
    postaction={decorate}
    },
mdad/.style={decoration={markings, mark=at position 0.3 with {\arrow{stealth}}}, 
             postaction={decorate}},
point/.style={node distance=2cm, inner sep=0pt, fill=black, circle}]

\node[point] (p1) {.} ;
\node[point, left of=p1, yshift=-1.4cm](p2){.};
\node[point, below of = p1] (p3) {.}; 
\node[point, right of=p1, yshift=-1.4cm](p4){.};
\node[point, below of = p3, yshift=0.7cm](p5){.};
\node[point, below of = p5, yshift=0.4cm](p7){.};
\node[point,left of=p7, xshift=0.3cm] (p6) {.};
\node[point, right of=p7,  xshift=-0.3cm] (p8) {.};
\node[point, below of = p7, yshift=0.7cm](p9){.}; 
\def\myadjmat{%
{0,1,1,1,0,1,0,1,0},
{0,0,0,0,1,1,1,0,1},
{0,1,0,1,1,1,0,1,1},
{0,0,0,0,1,0,1,1,1},
{0,0,0,0,0,1,0,1,0},
}

\foreach \x[count=\xi] in \myadjmat{
  \foreach \y[count=\yi] in \x{
    \ifnum1=\y\relax\draw[mdar] (p\xi) -- (p\yi);\fi
  }
}

\end{tikzpicture}
\end{document}

I got bored after the fifth but you get the idea. Also don't leave the \usetikzlibrary{...} commands in the picture. Instead carry them to your preamble. Finally you might consider skipping the \tikzstyle command as it is deprecated as per Should \tikzset or \tikzstyle be used to define TikZ styles?

Here's an example with the graph drawing stuff. The node positioning is not amazing, but can be changed fairly easily. It can be complied "as usual" with pdflatex (or xelatex, or latex -> dvipdfm, etc).

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{graphs,decorations.markings}
\tikzgraphsset{on edge arrow/.style={/tikz/every edge/.append style={
  -, draw, postaction={
  decoration={markings, mark=at position \arrowpos with {\arrow{stealth}}},
  decorate}}}, > pos/.store in=\arrowpos, > pos=0.5}
\begin{document}
\begin{tikzpicture}[x=0.75cm,y=0.75cm]
\foreach \p [count=\i] in {(0,0),(-2,-1),(0,-1.75),(2,-1),(0,-3),
    (-1.5,-4.5),(0,-4.5),(1.5,-4.5),(0,-6.25)}
  \node [shape=circle, inner sep=0, minimum size=2,fill] (\i) at \p {};
\graph [use existing nodes, on edge arrow]{
    1 -> {2, 3, 4};
    2 -> {5 -> {6, 7, 8}, 6, 7 -> 9};
    3 -> {2, 4 -> {5, 7, 8}, 5};
    1 ->[> pos=.45] {6, 8};
    3 ->[> pos=.45] {6, 8};
    {2, 4} ->[> pos=0.66] 9;
};
\end{tikzpicture}
\end{document}

Since your arrows have no regular pattern, it's hard to make a really concise code because there is not an actual rule that governs where the arrows should go to, and so on. So This is a slightly longer code than I wanted to write, but it's still pretty short.

Output

Code

\documentclass[margin=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.markings, arrows}

\tikzset{
    %mdar/.style={very thin,decoration={markings, mark=at position 0.45 with {\arrow{stealth reversed}}}, postaction={decorate}},
    mdad/.style={very thin,decoration={markings, mark=at position 0.45 with {\arrow[scale=.8]{stealth}}}, postaction={decorate}},
    point/.style={inner sep=.5pt, fill=black, circle}
}

\begin{document}
\begin{tikzpicture}

% Nodes
\foreach \points [count=\xi] in {
        (0,0),
        (-1,1),(0,1),(1,1),
        (0,2),
        (-1.2,3.3),(0,3),(1.2,3.3),
        (0,4)}{
    \node[point] (p\xi) at \points {};
}

% Arrows
\foreach \name/\dest in {%  
    2/{1},
    3/{1,2,4},
    4/{1},
    5/{2,3,4},
    6/{1,2,3,5},
    7/{2,4,5,6,8},
    8/{1,3,4,5},
    9/{2,4,6,7,8},
    }{%
    \foreach \ppp in \dest{
        \draw[very thin, mdad] (p\name) -- (p\ppp);
    }
}
\end{tikzpicture}
\end{document}