Absolutely. Thanks to wave-particle duality, gravity affects particles such as photons. We're not used to thinking of photons losing energy as they fight gravity, but gravitational redshift, as mentioned by wwalker3, is quite real.

Thanks to mass-energy equivalence, your choices for visualizing this are many. Perhaps the two easiest are: Physically lifting the 1kg matter+antimatter to elevation h, which is equivalent to Gravitational redshifting of the 1kg-worth (converted to energy) of photons between ground level and elevation h

As an aside, if momentum is conserved, shouldn't each photon be paired and emitted in opposite directions? The author charitably attributes the inability for such a system to be energy neutral to "engineering problems," but I think it's pretty clear that there are also physical laws that make this impossible.