Nope, the "Adversary's Haunt" is the Scrin tower, "He" is Kane.
Or that's my reading, at least.
Edit: because while Kane may have a (small) force that could reach Philadelphia station, they'd have a tough time actually doing damage, or taking it.
And, Kane seems to be sitting this one out.
Very possible that Adversary"s Haunt is the Scrin tower as it is gigantic with the height being in the double digit kilometers which does make him reign over the Earth in a sense.
Unlikely, very unlikely, if Kane had a small infantry force that could reach Philadelphia station successfully, they would not have tough time doing severe damage as we have seen Commandoes on both sides destroy Structures which they can carry by themselves or the Walkers like the Avatar or the Scrin Walker during the Campaign. As for taking damage it depends on whether they are using cybernetics or not heavily as if they do they could easily send the cyborgs which are as durable as the enlightened which can withstand a mammoth tank round to the face without breaking stride, making them effectively immune to most weapons on the Station.