When you use \csname gather*\endcsname, amsmath is smart enough to know what environment's name it has been called in, so as to absorb all text until the corresponding \end command appears. With your code it determines to have been called in minipage, but it's not able to see \end{minipage}, that's buried inside the end code.
So, just like Dan proposes, you can use \minipage and \endminipage. But this will not give a good output (I added \fbox around it just to clearly show the problem):

Why's that? Because you're starting a paragraph with a display, which shouldn't be done.
A workaround is to back up by \baselineskip
\documentclass[border=6pt]{standalone}
\usepackage{amsmath}
\newenvironment{mygather}
{%%
\minipage{2in}
\vspace{-\baselineskip}
\csname gather*\endcsname
}{%%
\csname endgather*\endcsname
\endminipage
}
\begin{document}
\fbox{\begin{mygather}
y = x^{2} - 3x + 5
\end{mygather}}
\end{document}

A simpler way is
\documentclass[border=6pt]{standalone}
\usepackage{amsmath}
\newenvironment{mygather}
{%%
\minipage{2in}
\centering$\!\gathered
}{%%
\endgathered$
\endminipage
}
\begin{document}
\fbox{\begin{mygather}
y = x^{2} - 3x + 5
\end{mygather}}
\end{document}
alignwithin a custom environment with amsmath, but I can't find it right now. I think that the solution was to use theenvironpackage. – Andrew Stacey May 28 '14 at 16:57equationandsplit. – Werner May 28 '14 at 17:43gatheredenvironment defined in themathtoolspackage. that's meant as a subsidiary environment, whichgatheris not. – barbara beeton May 28 '14 at 18:20mathtools. Ultimately I've chosen to go with theenvironpackage. – A.Ellett May 28 '14 at 19:10