I guess one answer to this is that particles which are (supposedly?) massless, like the photon, are affected by the space-time warping effects of gravity. A parallel construction wouldn't be true of magnetism or an electric field. Furthermore, when we detect gravity waves, they come at the same time as corresponding gamma ray bursts; since the gamma rays are affected by the space-time warping effects of gravity, this means that the gravity waves themselves are affected by the space-time warping effects of gravity.

So gravity probably is something else. But who knows!