I completely loathe anime with every cell of my body, so you'll never catch me with an avatar like that, but I do understand why many people have them. A lot of video game fans simply also like anime. I'm not sure why there's such a strong overlap (I guess because video games and anime are both often lumped together as "nerdy" things?), but there is an overlap nonetheless.
Also, the difference between the anime "style" of illustration and most other types of drawing and illustration is that characters in anime tend to have more realistic proportions than other cartoons (there exist exceptions of course), making anime characters feel more "attractive" than many other exaggerated styles of cartoon drawings. It makes sense that such characters should appeal to people more.