Earlier quoted context omitted.
"Lovecraftian" is still used as a general term for an entire genre of fiction. He was a xenophobe, but that is not what he's best known for. Similarly, Aristotle was a misogynist, but it would not be accurate to say that Aristotle is best known as a navel-gazing misogynist.
I think it's a bit more complicated than that. Lovecraft is fundamentally about confronting modernism and the inevitable decay of humanity in the faces of forces beyond our control. Central to that is the decay of the Anglo-Saxon genetic stock. Xenophobic isn't quite the right word. Racist is closer, but even that misses the mark. Every story he writes is terrified of black voodoo savages, or toothless white hill peo…
I do think you're right that Lovecraft's ability to write effective horror was largely because he himself was fascinated with terror at the world. But I don't think his weird xenophobia is what he ended up actually communicating to most readers or what he's famous for. He's more known for misshapen tentacle monsters and cosmic-scale horror. For example, Lauren Beukes' novel Broken Monsters is often considered Lovecraftian horror, and it has fairly modern sensibilities.