First point is that the term is an English translation of the original. From the Publisher's Note, page viii:
...
--The papers were originally published by the
Querido Verlag in Amsterda. In fairness to Professor
Einstein, his American publishers would like to make
it clear that although they have his full authorization
to translate the German text as published in Holland,
and although the documents from which the original
publication was made have his authentication, there
has been no further collaboration by him.
...
The subject term is at the end of the passage quoted below.
From page 82 Essays in Science, essay Notes On The Origin Of The General Theory Of Relativity, by Albert Einstein, published 1934:
--A material point, which is acted on by no force,
will be represented in four-dimensional space by a
straight line, that is to say by a line that is as
short as possible or more correctly, an extreme line.
This concept presupposes that of the length of a linear
element, that is to say, a metric. In the special theory
of relativity, as Minkowski had shown, this metric was a
quasi-Euclidean one, i.e., the square of the "length" ds
of the linear element was a definite quadratic function
of the differentials of the co-ordinates.
If other co-ordinates arrew introduced by means of
a non-linear transformation, ds² remains a homogeneous
function of the differentials of the co-ordinates, but
the co-efficients of this function (guv) cease to be
constant and become certain functions of the co-ordinates.
In mathematical terms this means that physical (four-dimensional)
space has a Riemannian metric. The time-like extremal
lines of this metric furnish the law of motion of a material
point which is acted on by no force apart from the forces
of gravity.
What is the meaning of "time-like?"