Run DMC did have an influence on NYC-based hip hop, but that's about it; even then, their influence only lasted a couple of years (unless you want to get into the rap-rock thing, but then the Beastie Boys had as much a hand in that).
But yeah, gangsta rap was born in '88 with Straight Outta Compton. N.W.A.'s defining moment birthed a popular genre that still exists/sells over 16 years later. Run DMC can speciously lay claim to a genre that was bastardized by the time the fucking Judgment Night soundtrack came out over a decade ago, and hasn't been about rap since, anyway.