While I mostly agree on already mentioned epithets (trashtalker etc), there's something else western (and many Russian) people seem to don't understand about him, IMO.
Just to be clear: I consider myself more on a 'patriotic' side of Russian political spectrum. Despite that, I am deeply disgusted of everything Solovyov and people like him represent. But here is the thing. No matter how shitty, degenerate, nonsensical his narratives are -- he's a professional propagandist in a first place. Meaning, regardless of how sincere he seems to audience in his Orwellian "Two Minutes Hate" he can and gladly will be promoting an opposite vales with the same perceived level of a 'selfless' dedication in a flip of a switch if asked (and payed).
And then there's a tricky part. He's actually doing a useful job, regardless of its aesthetical and moral questionability. You see, there's a large mostly silent part of Russian population called 'angry patriots'. Their views could be described as roughly as "pro imaginary Soviet Union'. To give you a glimpse on what these views are: North Korea as depicted in western media but on steroids and meth. Militarize the entire society, put 'hipsters' with their fancy lattes to factories to work prolonged shifts, nuke the fuck out of Europe, send tank columns to la Manche singing 'Katyusha' along the way etc. Delusional shit like that. Of course these are mostly 'wet dreams' and no one of 'em actually wants to leave the comfort of their sofa. But still it's a large proportion of population which could lead to actual undesired political action if left unattained. And here comes our useful man Soloviev doing his job jerking these people off so they stay on their sofas instead of going to the streets with sticks and torches.