It's not clear what you think needed doing manually, but just using ybar stacked and plotting each piece works fine here.
For the totals atop the bars, we can use \addplot+[nodes near coords] for the last plot in the stack as shown in Stacked bar-plot: display total value. However, in pgfplots v1.9 and later, some extra code is added to modify the behavior of nodes near coords for the stacked bar plot types. This is discussed at the end of section 4.5.9 in the manual.
For most bar plots, these modifications make sense and are reasonable. But they are not wanted here. So, we can override the modifications by emptying an internal style used by pgfplots sometime before setting ybar stacked. This in general looks like
\pgfplotsset{nodes near coords ybar stacked configuration/.style={}}
and it can be set locally or globally in the document depending on how widespread its effect needs to be.
Here's the complete code:
\documentclass[tikz]{standalone}
\usepackage{pgfplots,pgfplotstable}
\pgfplotsset{compat=1.12}
\pgfplotstableread[col sep=comma,header=true]{
Year,RoW,MEA,China,Americas,APAC,Europe
2000,751,0,19,21,368,129
2001,807,0,24,24,496,265
2002,887,0,42,54,686,399
2003,964,0,52,102,916,601
2004,993,1,62,163,1198,1306
2005,1003,1,70,246,1502,2291
2006,1108,1,80,355,1827,3289
2007,1150,2,100,522,2098,5312
2008,1226,3,140,828,2628,11020
2009,1306,25,300,1328,3373,16854
2010,1590,80,800,2410,4951,30505
2011,2098,205,3300,4590,7513,52764
2012,2098,570,6800,8365,12159,70489
2013,2098,953,18600,13727,21992,81464
}\data
\begin{document}
\begin{tikzpicture}
\begin{axis}[
nodes near coords ybar stacked configuration/.style={}, % disable modifications
ybar stacked,
]
\addplot table[x=Year,y=China] from \data;
\addplot table[x=Year,y=Americas] from \data;
\addplot table[x=Year,y=APAC] from \data;
\addplot+[nodes near coords] table[x=Year,y=Europe] from \data;
\end{axis}
\end{tikzpicture}
\end{document}
Of course, the axis/tick labels, spacing, and other stuff needs changing to match the desired result, but all of this is doable. I think your question is rather focused on the stacking of the bars themselves.
And the result:

Edit 3: Another request was added in a comment for no scientific notation in the nodes near coords labels. The style of those nodes is determined by the every node near coord style, which is initially empty. We can disable scientific notation using the standard number-printing style pgf/number format/fixed. Here I've also shown decreasing the font size of those labels by also adding node font=\scriptsize:
\documentclass[tikz]{standalone}
\usepackage{pgfplots,pgfplotstable}
\pgfplotsset{compat=1.12}
\pgfplotstableread[col sep=comma,header=true]{
Year,RoW,MEA,China,Americas,APAC,Europe
2000,751,0,19,21,368,129
2001,807,0,24,24,496,265
2002,887,0,42,54,686,399
2003,964,0,52,102,916,601
2004,993,1,62,163,1198,1306
2005,1003,1,70,246,1502,2291
2006,1108,1,80,355,1827,3289
2007,1150,2,100,522,2098,5312
2008,1226,3,140,828,2628,11020
2009,1306,25,300,1328,3373,16854
2010,1590,80,800,2410,4951,30505
2011,2098,205,3300,4590,7513,52764
2012,2098,570,6800,8365,12159,70489
2013,2098,953,18600,13727,21992,81464
}\data
\begin{document}
\begin{tikzpicture}
\begin{axis}[
nodes near coords ybar stacked configuration/.style={}, % disable modifications
ybar stacked,
every node near coord/.style={node font=\scriptsize,/pgf/number format/fixed},
]
\addplot table[x=Year,y=China] from \data;
\addplot table[x=Year,y=Americas] from \data;
\addplot table[x=Year,y=APAC] from \data;
\addplot+[nodes near coords] table[x=Year,y=Europe] from \data;
\end{axis}
\end{tikzpicture}
\end{document}

pgfplotsadded some modifications to the code for this style of plot, which needs to be overridden to produce your desired result. – Paul Gessler May 01 '15 at 12:51