When someone thinks they are the main character of their life. Usually comes with a side of individuality complex, quirky style and a self centered point of view.

A male who is consistently kissing another man's ass in attempt to gain his acceptance, laughs a little too loud at jokes in an attempt to fit in, seems to mold himself out of another man he admires <scary!> wanting to be just like another dude so much it gets to the point where it becomes an abnormal obssession that causes his idol to try to avoid him and his idol's girlfriend to get freaked out by the dick rider's clinginess.

All of these definitions are wrong, or half there.

A dick rider is a person who is usually and overzealous mindless fan of anyone(be it a rapper, singer, athlete, music genre, band, or any given thing). A dick rider see's no flaw in whatever they are dick riding at the time, and if you happen to offer an opinion or simply not like whatever a dick rider likes, the dick rider will consider your a "hater" for offering your opinion.

Most of the times dick riders are female fans of a band, rapper, or singer who constantly praises the graces of a music artist they never met, or are going to touch in that star's fame . Male dick riders are usually men who want to be or picks up the "swag" and attitude of their favorite artist, and they'll swear that's how they are(this is usually a phenomenon in the hip-hop culture)

someone who is a follower not a leader

Those who constantly rides dirt bikes and thinks that they are superior to everyone else because of it. They are also known to be racist, reckless, Trump supporters, jackasses, perverts diesel truck lovers, and frequently wear rock revival jeans.

Someone who "sucks up" to one another, always agreeing with that person for something in return i.e. power. Thus, they are "riding" that individual's dick.