We know it exists because it does interact with gravity.
More accurately, we believe with high probability that it exists because our observations show that the rotation of stars in galaxies don't behave consistently with the amount of visible matter we can see, assuming that we've correctly calculated the universal gravitational constant (from observations of the solar system), that it's actually a universal constant, and that general relativity is correct.
Maybe there's another explanation. But dark matter fits really, really well with the rest of our observations, without breaking everything else we believe we know.
I didn't know until this thread that this character is from Overwatch or that there is apparently a lot of porn of her. I only knew it as a random meme format.