  In this paper we show the statement in the title. To any Garside group of
finite type, Wiest and the author associated a hyperbolic graph called the
\emph{additional length graph} and they used it to show that central quotients
of Artin-Tits groups of spherical type are acylindrically hyperbolic. In
general, a euclidean Artin-Tits group is not \emph{a priori} a Garside group
but McCammond and Sulway have shown that it embeds into an \emph{infinite-type}
Garside group which they call a \emph{crystallographic Garside group}. We
associate a \emph{hyperbolic} additional length graph to this crystallographic
Garside group and we exhibit elements of the euclidean Artin-Tits group which
act loxodromically and WPD on this hyperbolic graph.
