Good topic.
This is definitely a contributing factor, I think. I know there's a thread floating somewhere around here talking about the way that a lot of fans of VK seemed to have transitioned over to K-Pop over the years. I think a lot of it has to do with the the whole 'pretty Asian boys' fetish (maybe 'fetish' is a slightly strong word, but you guys know what I mean). K-Pop in general takes the whole cute Asian boy thing and ramps the production values up to to 11, whilst also presenting itself as a more mainstream and socially acceptable thing to be into. It's no surprise that a lot of foreigners mostly looking for their cute Asian boy fix would slowly have migrated over to the K-Pop scene once that started getting popular in the early 2010's, which coincidentally just so happens to be when VK's decline took hold according to that Google trends result.
Also a very good point. I'd say this combined with the previous point definitely contributed to some degree.
I find this graph particularly interesting. I have to second what @Zeus said previously; the so-called decline of VK does seem, in many ways, more to be a simple case of its western popularity declining after a short boom. In that respect it's really nothing too surprising, a lot of rapid booms in the popularity of a concept or thing tend to be associated with equally as rapid declines. The real thing to note is that its prevalence in Japan has remained relatively stable, so the scene itself probably hasn't changed all that much in domestic terms.
Another theory I'll put forward though, and I'll admit not everyone with agree with me as this is a pretty subjective viewpoint, is that the quality of Visual Kei music simply hasn't been good enough in recent years. It feels like there are still shittons of bands out there, but almost no truly great ones; ones that you just feel you HAVE to pay attention to. Once upon a time you had the likes of D'espairsRay, Kagrra, Miyavi (still around but not VK), the GazettE (still around but a shadow of their former selves IMO), Rentrer en Soi, 9GBO, etc. Nowadays there are very few bands, if any, that are on levels similar to those groups. I'm sure there will be quite a few people that disagree with me here, but I've seen similar sentiments expressed by other members too, so I know I'm not the only one who thinks this way.
Silly tl;dr - The popularity of Visual Kei internationally reached its peak when the GazettE reached their creative peak in mid 2009; since then the band's creative quality has fallen into oblivion. To cope with the disappointment, western VK fans began listening to K-Pop after hearing BIGBANG's FANTASTIC BABY around the same time Gazetto released that garbage DIVISION album, and decided that G-Dragon oppa was the new saviour of cute Asian boy music. Thus VK died an agonizing death. Also, MEJIBRAY.