In the end, this is the code (replacing lines 46-55 of beamerinnerthemeArguelles.sty)that best replicated the results using the enumitem package. It requires the package xpatch. There is still some difference with the handling of description environments, but hopefully itemize and enumerate environments look faithful to the original theme.
\setbeamertemplate{itemize item}{$\bullet$}
\setbeamertemplate{itemize subitem}{$\circ$}
\setbeamertemplate{itemize subsubitem}{$\cdot$}
\setbeamertemplate{enumerate item}[default]
\setbeamertemplate{enumerate subitem}{\theenumi.\theenumii.}
\setbeamertemplate{enumerate subsubitem}{\theenumi.\theenumii.\theenumiii.}
\setbeamertemplate{description item}{\normalfont\itshape\insertdescriptionitem}
\AtBeginEnvironment{itemize}{
\settowidth{\leftmargini}{\usebeamertemplate{itemize item}}
\addtolength{\leftmargini}{\labelsep}
\settowidth{\leftmarginii}{\usebeamertemplate{itemize subitem}}
\addtolength{\leftmarginii}{\labelsep}
\settowidth{\leftmarginiii}{\usebeamertemplate{itemize subsubitem}}
\addtolength{\leftmarginiii}{\labelsep}
}
\xpatchcmd{\itemize}
{\def\makelabel}
{\ifnum@itemdepth=1\relax
\setlength\itemsep{0em}% separation for first level
\else
\ifnum@itemdepth=2\relax
\vspace{-0.5em}
\setlength\itemsep{-0.5em}% separation for second level
\else
\vspace{-0.5em}
\ifnum@itemdepth=3\relax
\setlength\itemsep{-.5em}% separation for third level
\fi\fi\fi\def\makelabel
}
{}
{}
\xpatchcmd{\beamer@enum@}
{\def\makelabel}
{\ifnum@itemdepth=1\relax
\setlength\itemsep{0em}% separation for first level
\else
\ifnum@itemdepth=2\relax
\vspace{-0.5em}
\setlength\itemsep{-0.5em}% separation for second level
\else
\vspace{-0.5em}
\ifnum@itemdepth=3\relax
\setlength\itemsep{-.5em}% separation for third level
\fi\fi\fi\def\makelabel
}
{}
{}