In this work, a quantum self-test which certifies that measurements of a quantum device have a large Gowers norm of order k is presented and analysed. The test protocol is described as a two-player quantum game, in which players provide answers based on measurements on subsystems of a maximally entangled bipartite state. The protocol makes use of 2k +1 subtests. It is shown that strategies that succeed in the test with success rate 1-E must have a Gowers norm larger than 1-O(E). This test generalizes measurement tests that certify measurements based on the second order Gowers norm.