Wilson's piece is dripping with metaphysical turns of phrase, but much of what she says could be re-expressed in a conceptual or linguistic key. I think this goes for a good deal of contemporary metaphysics. However, converting metaphysically-expressed ideas and claims into a conceptual or linguistic key may make them a bit fiddlier to think and express. And if you're doing hard philosophy and need to think and express a lot of things, this extra cost is going to pile up. Sometimes, having things in a conceptual or linguistic register may make things clearer, and sometimes it may be essential. But for many purposes the metaphysical register does fine, and often has the benefit of being less resource-hungry.
Yes, some metaphysics may not be capturable in conceptual or linguistic terms, and perhaps even in favourable cases the capturing will not be complete or perfect. And there are doubtless other important things going on behind the sociological phenomenon of the resurgence of metaphysics. But maybe this is part of the story.
UPDATE: Brandon Watson (at the end of a post on Fitch's paradox) links to this post, writing: 'I'm very interested, of course, in accounts of how philosophical scenes get transformed, how ideas transmogrify, and the like. This hypothesis for the rise of analytic metaphysics makes considerable amount of sense, and is probably true.' This is encouraging! I might try to develop this idea a bit further some time.