Well the REASON he's leading the horde officially is because He's a direct descendant of Grom Hellscream, which made Thrall have a Fangirl Moment for him and promote him to one of the highest military ranks acheiveable next only to Saurfang and Thrall himself. So when Thrall left he said "Hey Garroshy-woshy... wanna lead the horde?" Then Garrosh sipped his beer and said "Sure, lemme get my nipples enlarged first though." And that's how it all happened.