Heh, about time this came up again for it's annual airing
It's clearly nothing to do with the race of the artist, as previous award winners including such famous black people as Eminem, Jamie Cullum, Amy Winehouse, Justin Timberlake, Christina Aguilera...etc
It's called MOBO, because most people think hip-hop, r&b etc is music of black origin, so as a catchy name for an awards ceremony about genres of music like hip-hop, r&b etc they decided to call it the Music of Black Origin awards which conveniently can be condensed to a catchy acronym of MOBO.
On the other hand, Music of White Origin doesn't really mean anything to most people, so even if you had a 'MOWO' awards, you'd have to first pick a bunch of 'white' genres, and collect them all together ending up in a slightly bizarre hotchpotch of genres, so it's quite likely people wouldn't be interested in any event.