Below is the Dutch paper mentioned by Francois Ziegler; This paper did indeed appear before the 1927 paper mentioned in the OP, but Van der Waerden does refer to that forthcoming publication in a footnote; I translate:
This theorem is a special case of the "Nulpuntenstelling" van HILBERT$^{5})$
$^{5})$ Hilbert assumes that $\Omega$ is the field of complex numbers; his proof actually holds more generally. For a different proof see my forthcoming paper in the Mathematische Annalen entitled "Zur Nullstellentheorie der Polynomideale".
The Mathematische Annalen paper was submitted 14 August 1925, while the paper below was read at the Netherlands Akademy on 28 November 1925, which explains why Van der Waerden could refer to former as a an earlier work.
B.L. Van der Waerden, Een algebraies kriterium voor de oplosbaarheid van een stelsel homogene vergelijkingen, Verslag van de Gewone Vergadering van de Afdeling Natuurkunde van de Koninklijke Akademie van Wetenschappen 34, 1123-1130 (1925)
[source] -- only accessible online from a US IP number.