A key part of Lovecraft's work is that the universe is _not_ centered around the human race. In his cosmology, we are small and insignificant and the unverse does not care about us. Get outside of our tiny bubble of ignorance and we will be overwhelmed to the point of madness.
And one of the way that Lovecraft expressed that idea was by making his aliens fundamentally different than humans. His alien races aren't human beings with a few cosmetic differences but creatures that are so inhuman they sometimes don't even follow the same laws of physics.
Lovecraft's elder things actually helped inspire the term starfish alien to describe an alien that is intrinsically different than us. A combination of plant and animal qualities and pentagram symmetry, the elder things' heads and feet actually look like starfish.
And the elder things are one the aliens that can most closely relate to the human race! You have the fungi mi-go that don't exist entirely in regular dimensions. Cthulhu and his fellow great old ones are actually aliens, but so different and on such a different scale they are like gods to people.
But the Colour Out of Space takes the cake. Whatever is going on in the story is so different that you could even argue that there might not even be an alien in the story. No one even interacts with the strange force, they just observe it and are affected by it.
The plot itself is simple. A meteorite lands near an isolated farm and a mysterious force from it twists and absorbs the life of everything around until it's strong enough to go back to the stars. The story may have helped make that a stock plot.
For most of the story, the meteorite could as easily have caused groundwater contamination instead of brought an alien life. Animal and plant life grows wild but deformed, followed by serious degradation. It could easily be seen as radiation poisoning. Not until a strange aura of a color outside the normal spectrum rises out of the well and to the stars do we really get a good argument that the story is dealing with alien life.
In addition to being utterly unearthly, the life form in the Colour Out of Space also stays mysterious because Lovecraft doesn't explain anything. He just shows us the results of its activity or existence.
With this story, Lovecraft didn't just create a fun yearn. He created an example of how to show an alien life form being truly and profoundly alien.